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This work investigates a state estimation problem for linear time-invariant systems based on polarized measurement information from event sensors. To enable estimator design, a new notion of observability, namely,\epsilon-observability is defined with the precision parameter\epsilon which relates to the worst-case performance of inferring the initial state, based on which a criterion is developed to test the\epsilon-observability of discrete-time linear systems. Utilizing multisensor polarity data from event sensors and the implicit information hidden in event-triggering conditions at no-event instants, an iterative event-triggered state estimator is designed to evaluate a set containing all possible values of the state. The proposed estimator is built by outer approximation of intersecting ellipsoids that are predicted from previous state estimates and the ellipsoids inferred from received polarity information of event sensors as well as the event-triggering protocol; the estimated regions of the state derived from multisensor event measurements are fused together, the sizes of which are proved to be asymptotically bounded. Distributed implementation of the estimation algorithm utilizing a two-layer processor network of hierarchy architecture is discussed, and the temporal computational complexity of the algorithm implemented in centralized and distributed ways is analyzed. The efficiency of the proposed event-triggered state estimator is verified by numerical experiments. [ABSTRACT FROM AUTHOR]

This article is concerned with the identification of time‐varying systems. Differently from the conventional polynomial approximation approaches, the changing laws of the time‐varying parameters are considered to build the identification model for the time‐varying systems. Specifically, the concept of the invariant matrix is put forward to characterize the time‐varying parameters and to establish the state‐space model with regard to the system parameters. Then this article proposes a stacked state estimation algorithm to achieve the time‐varying parameter estimation. Moreover, for the purpose of enhancing the computational efficiency, a detached state estimation algorithm is proposed by reducing the dimension of the state vector to reconstruct the state equation. Finally, a numerical simulation example is employed to demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper introduces a new reduction method for linear time-invariant continuous and discrete-time systems. The method is created considering only the effect of the dominance pole to get the reduced-order model. The denominator coefficient of reduced order model (ROM) is obtained by conserving the dominant poles of a higher order system while the numerator polynomial of the reduced model is found by comparing the original system transfer function with the transfer function of desired reduced order model. Five standard numeric examples are examined from literature considering single input single output (SISO) and discrete systems. To prove the validity, accuracy and simplicity of the proposed method, the results obtained are compared with other recent established and well-known techniques like Truncation and Routh Stability methods. [ABSTRACT FROM AUTHOR]

We address the problem of determining optimal sensor precisions for estimating the states of linear time-varying discrete-time stochastic dynamical systems, with guaranteed bounds on the estimation errors. This is performed in the Kalman filtering framework, where the sensor precisions are treated as variables. They are determined by solving a constrained convex optimization problem, which guarantees the specified upper bound on the posterior error variance. Optimal sensor precisions are determined by minimizing the $l_1$ norm, which promotes sparseness in the solution and indirectly addresses the sensor selection problem. The theory is applied to realistic flight mechanics and astrodynamics problems to highlight its engineering value. These examples demonstrate the application of the presented theory to 1) determine redundant sensing architectures for linear time invariant systems, 2) accurately estimate states with low-cost sensors, and 3) optimally schedule sensors for linear time-varying systems. [ABSTRACT FROM AUTHOR]

Summary: In system identification, prior knowledge about the model structure may be available. However, imposing this structure on the identified model may be nontrivial. A new discrete‐time linear time‐invariant identification method is presented in the article that imposes prior knowledge of the degree of the common denominator of the system's transfer function matrix and the degrees of the numerators. First, a method is outlined for the solution in case of exact data. Then, this method is extended for noisy data in the output error setting. An initial estimate obtained by a subspace method is improved by a structured low‐rank approximation method. The performance of the method imposing the structure is compared on simulated data with the performance of classical identification methods that do not impose the structure. [ABSTRACT FROM AUTHOR]

This article investigates two On-policy and Off-policy Q-learning algorithms for time-varying linear discrete-time systems (DTSs) in the presence of complete dynamic uncertainties. To handle the challenge of time-varying description, the lifting method is employed to transform the original time-varying linear DTS into time-invariant linear DTS in the absence of the conventional controllability condition, which affects to the convergence of traditional Q-learning algorithms. Based on theoretical analysis of the structure in the obtained time-invariant linear DTS, On-policy and Off-policy algorithms are proposed to guarantee the convergence of Q-learning algorithms. Both On-policy and Off-policy Q-learning algorithms guarantee model-free consideration under the data collection. Especially, the Off-policy technique is able to develop the algorithm with high data efficiency because the collected data can be utilized again after each iteration. Finally, the simulation results of two-dimensional systems and spacecraft control systems are presented to validate the effectiveness of the two proposed control schemes. [ABSTRACT FROM AUTHOR]

This article introduces the notion of absolutely distinguishable discrete‐time dynamic systems, with particular applicability to linear time‐invariant and linear parameter‐varying systems. The motivation for this novel type of distinguishability stems, in particular, from the stability and performance requirements of worst‐case adaptive control methodologies. The main results presented herein show that, in most practical cases, a persistence of excitation type of condition and a minimum number of iterations are required to properly distinguish two dynamic systems. We also demonstrate that the former constraint can be written as a lower bound on the intensity of the exogenous disturbances. The applicability of the developed theory is illustrated with a set of examples. [ABSTRACT FROM AUTHOR]

A methodology for the synthesis of time-varying static output-feedback gains, capable of stabilising continuous-time linear time-varying systems, is proposed in this paper. The method is based on the computation of output-feedback gains that stabilise a family of periodic discrete-time subsystems, related to the original model, followed by a transformation that yields the desired stabilising gains for the continuous-time system. Based on such strategy, three different approaches to compute stabilising periodic discrete-time gains, as well as the necessary transformations to generate the continuous-time output-feedback gains, are proposed. Numerical examples are presented in order to compare and analyze the efficiency of the proposed approaches. [ABSTRACT FROM AUTHOR]

In this paper, a model-based prognosis method where the degradation cannot be directly measured but only detectable through the drift of a model parameter is considered. This parameter drift is viewed as an unknown input, whose reconstruction allows the estimation of the degradation state. Model-based prognosis is divided into a filtering step where the current degradation state is estimated, and an uncertainty propagation step where the future degradation state is predicted. During these two steps, model uncertainty and measurement uncertainty are taken into account within the set-membership framework using interval techniques. The filtering step is performed with an interval unknown input observer for linear time-invariant discrete systems. Then, based on a set-membership constraint satisfaction methodology, interval propagation is performed to estimate the bounds that include the future degradation state until some failure threshold is reached, allowing the deduction of the interval including the remaining useful life. In order to demonstrate the efficiency of the proposed model-based prognosis methodology, the degradation of a suspension system is studied. [ABSTRACT FROM AUTHOR]

Summary: This article introduces a new nonlinear observer for state estimation of linear time invariant systems. The proposed observer contains a (nonlinear) cubic term to enhance observer response. Unlike previously proposed observers, the cubic observer has nonlinear estimation error dynamics. Convergence criteria, performance advantages, and observer‐based feedback control with cubic observers are addressed. Simulation examples demonstrating performance improvement compared with linear observers, are included. [ABSTRACT FROM AUTHOR]

Motivated by the increasing availability and quality of miniaturized sensors, computers, and wireless communication devices and given their enormous potential, the use of wireless sensor networks (WSN) has become widespread. Because in many applications of WSNs one is required to estimate at each local sensor unit the state of a system given the measurements acquired by multiple sensors, there has been a flurry of activity related to the theory of distributed state estimation. This article contains a literature survey of distributed state estimation for discrete-time linear time invariant systems. In order to obtain the proper historical context, we review the state of the art in this field and summarize previous work. To provide the mathematical intuition behind some of the methods, this survey paper reproduces some of the main results given in the literature. It also provides a critical appraisal of the state of the art and affords the reader a comprehensive presentation of the most relevant results published so far. [ABSTRACT FROM AUTHOR]

The problem of synchronization of multiple linear time-invariant systems connected over a network with asynchronous and intermittently available communication events is studied. To solve this problem, we propose a controller with hybrid dynamics, namely, the controller utilizes information transmitted to it during discrete communication events and exhibits continuous dynamics between such events. Due to the additional continuous and discrete dynamics inherent to the interconnected networked systems and communication structure, we use a hybrid systems framework to model and analyze the closed-loop system. The problem of synchronization is then recast as a set stabilization problem and, by employing Lyapunov stability tools for hybrid systems, sufficient conditions for asymptotic stability of the synchronization set are provided. Furthermore, we show that the property of synchronization is robust to perturbations. Numerical examples illustrating the main results are included. [ABSTRACT FROM AUTHOR]

In this paper, we study the state estimation for a linear time-invariant (LTI) discrete-time system with quantized measurements. The quantization law under consideration has a time-varying data rate. To cope with nonlinearities in quantization laws and to analyse stability in the state estimation problem, a Kalman-filter-based sub-optimal state estimator is developed and an upper bound of its estimation error covariance is minimized. It turns out that, to guarantee the convergence of the upper bound, the averaged data rate of the quantization law must be greater than a minimum rate. This minimum data rate for the quantization law is presented in terms of the poles of the system and design parameters in the state estimator. Numerical examples are presented to illustrate the results in this work. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes a novel Krasovskii–LaSalle theorem for discrete-time switched linear time-invariant systems. The result is utilized to guarantee exponential convergence of both leaderless and leader-following consensus of discrete-time multi-agent systems under jointly connected switching network topology. Different from the continuous-time multi-agent systems under switching networks, where the magnitude of the dwell time of switching signals is irrelevant, in the discrete-time case, this value is critical for consensus reaching. A special index, called the constrained controllability index, is defined. This index can be easily calculated and provide a tighter lower bound of the dwell time when compared to those given in the literature. With our novel method, the controllability condition on the system matrix is relaxed to the stabilizability condition, and the proposed results not only expand the existing discussions to balanced switching networks but also cover some unbalanced networks. Finally, numerical examples and simulations are provided to verify the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is devoted to the problem of computing control laws for the stabilization of continuous-time linear time-varying systems. First, a necessary and sufficient condition to assess the stability of a linear time-varying system based on the norm of the transition matrix computed over a sequence of successive finite-time intervals is proposed. A link with a stability condition for an equivalent discrete-time model is also established. Then, 3 approaches for the computation of stabilizing state-feedback gains are proposed: a continuous-time technique, ie, directly derived fromthe stability condition, not suitable for numerical implementation; a method based on the stabilization of the discrete-time equivalent model along with a transformation to generate the desired continuous-time gain; and the computation of stabilizing gains for a set of periodic discrete-time systems. Finally, by adapting one of the existing methods for the stabilization of periodic discrete-time systems, an algorithm for the computation of a stabilizing state-feedback continuous-time gain is proposed. A numerical example illustrates the validity of the technique. [ABSTRACT FROM AUTHOR]

In this article, a new multidimensional discrete chaotic system is proposed, and the characteristics and advantages of the multidimensional discrete chaotic system are analyzed. The multidimensional discrete chaotic system is designed using digital technology, and the system has the complexity of hyper-chaotic system, and it can avoid the choice of step size, at the same time, the design of the circuit is simple, the resource occupancy rate is low, it is suitable for the design of digital system, and so on. It can be used in constructing chaotic sequence generator, chaotic encryption, and visual sensor networks. [ABSTRACT FROM AUTHOR]

This paper is concerned with the property of asymptotic hyperstability of a continuous-time linear system under a class of continuous-time nonlinear and perhaps time-varying feedback controllers belonging to a certain class with two main characteristics; namely, (a) it satisfies discrete-type Popov’s inequality at sampling instants and (b) the control law within the intersample period is generated based on its value at sampling instants being modulated by two design weighting auxiliary functions. The closed-loop continuous-time system is proved to be asymptotically hyperstable, under some explicit conditions on such weighting functions, provided that the discrete feed-forward transfer function is strictly positive real. [ABSTRACT FROM AUTHOR]

Fractional calculus increases their applications in system design and analysis problems because of providing more realistic modeling of real systems. Owing to computational complexity of fractional calculus, the computer-aided design and analysis methods are required for engineering applications of fractional order systems. This study presents a numerical method for parametric robust stabilization of fractional order systems by employing single-parameter perturbation. This method implements a fractional order perturbation strategy on the basis of brute-force search technique for system stabilization problems. In order to meet a predefined minimum argument root design specification, the proposed algorithm searches for a desired placement of the minimum argument characteristic root within the first Riemann sheet by performing iterative perturbations of the fractional order. This approach can provide a straightforward numerical solution for robust stabilization problems of fractional order systems by employing an order perturbation scheme. Moreover, a possible utilization of a fractional order derivative operator as a system stabilizer is theoretically discussed. Illustrative examples show the utilization of the proposed stabilization algorithms for computer-aided fractional order system design applications. [ABSTRACT FROM AUTHOR]

This paper proposes new iterative algorithms for the unknown input and state recovery from the system outputs using an approximate inverse of the strictly proper linear time-invariant (LTI) multivariable system. One of the unique advantages from previous system inverse algorithms is that the output differentiation is not required. The approximate system inverse is stable due to the systematic optimal design of a dummy feedthrough D matrix in the state-space model via the feedback stabilization. The optimal design procedure avoids trial and error to identify such a D matrix which saves tremendous amount of efforts. From the derived and proved convergence criteria, such an optimal D matrix also guarantees the convergence of algorithms. Illustrative examples show significant improvement of the reference input signal tracking by the algorithms and optimal D design over non-iterative counterparts on controllable or stabilizable LTI systems, respectively. Case studies of two Boeing-767 aircraft aerodynamic models further demonstrate the capability of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper proposes a novel lifting method which converts the standard discrete-time linear periodic system to an augmented linear time-invariant system. The linear quadratic optimal control is then based on the solution of the discrete-time algebraic Riccati equation associated with the augmented linear time-invariant model. An efficient algorithm for solving the Riccati equation is derived by using the special structure of the augmented linear time-invariant system. It is shown that the proposed method is very efficient, compared to the ones that use algorithms for discrete-time periodic algebraic Riccati equation. The efficiency and effectiveness of the proposed algorithm is demonstrated by the simulation test for the design problem of spacecraft attitude control using magnetic torques. [ABSTRACT FROM AUTHOR]

This paper is concerned with linear time-invariant (LTI) sampled-data systems (by which we mean sampled-data systems with LTI generalised plants and LTI controllers) and studies theirH2norms from the viewpoint of impulse responses and generalisedH2norms from the viewpoint of the induced norms fromL2toL∞. A new definition of theH2norm of LTI sampled-data systems is first introduced through a sort of intermediate standpoint of those for the existing two definitions. We then establish unified treatment of the three definitions of theH2norm through a matrix functionG(τ) defined on the sampling interval [0,h). This paper next considers the generalisedH2norms, in which two types of theL∞norm of the output are considered as the temporal supremum magnitude under the spatial 2-norm and ∞-norm of a vector-valued function. We further give unified treatment of the generalisedH2norms through another matrix functionF(θ) which is also defined on [0,h). Through a close connection betweenG(τ) andF(θ), some theoretical relationships between theH2and generalisedH2norms are provided. Furthermore, appropriate extensions associated with the treatment ofG(τ) andF(θ) to the closed interval [0,h] are discussed to facilitate numerical computations and comparisons of theH2and generalisedH2norms. Through theoretical and numerical studies, it is shown that the two generalisedH2norms coincide with neither of the threeH2norms of LTI sampled-data systems even though all the five definitions coincide with each other when single-output continuous-time LTI systems are considered as a special class of LTI sampled-data systems. To summarise, this paper clarifies that the five control performance measures are mutually related with each other but they are also intrinsically different from each other. [ABSTRACT FROM AUTHOR]

We address the global stabilization of linear time-invariant (LTI) systems when the magnitude of the control input and its successive time derivatives, up to an arbitrary order p ∈ N, are bounded by prescribed values. We propose a static state feedback that solves this problem for any admissible LTI systems, namely, for stabilizable systems whose internal dynamics has no eigenvalue with a positive real part. This generalizes previous work done for single-input chains of integrators and rotating dynamics. [ABSTRACT FROM AUTHOR]

The stability of the Kalman filter is classically ensured by the uniform complete controllability regarding the process noise and the uniform complete observability of linear time varying systems. This paper studies the case of discrete time output error (OE) systems, in which the process noise is totally absent. The classical stability analysis assuming the controllability regarding the process noise is thus not applicable. It is shown in this paper that the uniform complete observability is sufficient to ensure the stability of the Kalman filter applied to time varying OE systems, regardless of the stability of the OE systems. Though the continuous time case has been studied recently, the results on continuous time systems cannot be directly transposed to discrete time systems, because of a difficulty related to the observability of the discrete time filter error dynamics system. [ABSTRACT FROM AUTHOR]

A formal definition and design methodology for discrete-time higher-order sliding mode (DHOSM) based on finite difference method is proposed. A generalised reaching law is proposed to achieve r-order sliding mode in discrete time, and its behaviour and stability are analysed. The proposed reaching law is used to design a higher-order sliding mode control for an uncertain LTI system. The concept is experimentally validated on a real-time rectilinear plant and is compared with the existing algorithms on the basis of sensitivity function and (p, qr)-continuity. The results and comparison show that the proposed sliding algorithm has superior disturbance rejection capability as well as better continuity. This work is the first attempt to formally define and design DHOSM as opposed to discretisation of continuous time higher-order sliding mode. [ABSTRACT FROM AUTHOR]

We prove that for a class of zero-sum differential games with incomplete information on both sides, the value admits a probabilistic representation as the value of a zero-sum stochastic differential game with complete information, where both players control a continuous martingale. A similar representation as a control problem over discontinuous martingales was known for games with incomplete information on one side (see [P. Cardaliaguet and C. Rainer, Math. Oper. Res., 34 (2009), pp. 769-794]), and our result is a continuous-time analogue of the so-called splitting game introduced in [R. Laraki, Internat. J. Game Theory, 30 (2002), pp. 359-376] and [S. Sorin, A First Course on Zero-Sum Repeated Games, Springer, New York, 2002] in order to analyze discrete-time models. It was proved by Cardaliaguet [SIAM J. Control Optim., 46 (2006), pp. 816-838; J. Math. Anal. Appl., 360 (2009), pp. 95-107] that the value of the games we consider is the unique solution of some Hamilton-Jacobi equation with convexity constraints. Our result provides therefore a new probabilistic representation for solutions of Hamilton-Jacobi equations with convexity constraints as values of stochastic differential games with unbounded control spaces and unbounded volatility. [ABSTRACT FROM AUTHOR]

A novel order diminution method for linear time invariant continuous systems is proposed in this paper. The reduced denominator polynomial is obtained by modified clustering algorithm and the reduced numerator polynomial coefficients are generated by an evolutionary algorithm as referred in this communication. Several numerical examples taken from the literature have been solved for the validation of the proposed method. The reduced system obtained by proposed method guarantees the stability if the original system is stable and also preserves all characteristics of given higher order system in the reduced one. The presented method is to be continued to multivariable systems and illustrates with numerical examples for proving the efficiency of the proposed method. Furthermore, the proposed method is also to be extended for order reduction of discrete time systems. [ABSTRACT FROM AUTHOR]

In this paper, we address identification of a class of multi-input single-output (MISO) linear time-invariant (LTI) discrete-time systems, where the MISO system is composed of several single-input single-output (SISO) LTI systems and only the sum of the output of each SISO system can be measured. By exciting one SISO system and employing periodic inputs to the remaining SISO systems, we decompose the MISO system into the excited SISO system where its input and output can be calculated from the measured data. As such, the original parameters for each SISO system can be estimated using the well-established identification techniques. The proposed method using periodic inputs is also extended to identification beyond the Nyquist frequency. Both simulation and experimental results on identification of actuators in the dual-stage hard disk drive are carried out to demonstrate the efficacy of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we propose an approach for computing invariant sets of discrete-time nonlinear systems by lifting the nonlinear dynamics into a higher dimensional linear model. In particular, we focus on the maximal admissible invariant set contained in some given constraint set. For special types of nonlinear systems, which can be exactly immersed into higher dimensional linear systems with state transformations, invariant sets of the original nonlinear system can be characterized using the higher dimensional linear representation. For general nonlinear systems without the immersibility property, approximate immersions are defined in a local region within some tolerance and linear approximations are computed by leveraging the fixed-point iteration technique for invariant sets. Given the bound on the mismatch between the linear approximation and the original system, we provide an invariant inner approximation of the maximal admissible invariant set by a tightening procedure. [ABSTRACT FROM AUTHOR]

We study 2D systems with a continuous and discrete time axis. We embed known results about the stability and H ∞ -performance properties of such systems into multiplier theory from robust control. It is shown that this opens the way for applying recently developed gain-scheduled controller synthesis techniques in order to solve the H ∞ -design problem for 2D systems without any conservatism. This is presented if the discrete-time axis is either one- or two-sided, the latter leading to non-conservative H ∞ -synthesis result for infinite string interconnections of identical linear time-invariant systems. [ABSTRACT FROM AUTHOR]

This paper considers the recovery of sparse initial state for deterministic discrete-time linear time-invariant systems based on the compressed sensing theory. A class of deterministic linear systems with the global observation matrices satisfying the restricted isometry property (RIP) is characterized. Sufficient conditions on the measurement time instants that guarantee the global observation matrix to be a RIP matrix are obtained. With respect to the recovery of the sparse initial state of a high-dimensional linear system, it is worth mentioning that the number of measurements can be significantly decreased in terms of compressed sensing theory. [ABSTRACT FROM AUTHOR]

In this paper, the problem of robust discretisation of linear time-invariant (LTI) systems with polytopic uncertainties is introduced. More specifically, the main objective is to provide a systematic way to find an approximate discrete-time (DT) model of a continuous-time (CT) plant with uncertainties in polytopic domain. The system matrices of polytopic DT model to be found are expressed as parameter-dependent matrices which are homogeneous polynomials of arbitrary degree with respect to the uncertain variables in the simplex, and is obtained in such a way that the norm between the system matrices and the truncated power series of the exact DT model is minimised while preserving the polytopic structure of the original CT plant. The solution procedures proposed are presented in terms of single-parameter minimisation problems subject to linear matrix inequality (LMI) constraints which are numerically tractable via LMI solvers. Finally, examples are given to show the validity and effectiveness of the proposed techniques. [ABSTRACT FROM PUBLISHER]

This paper investigates asymptotic stability in probability and stabilization designs of discrete-time stochastic systems with state-dependent noise perturbations. Our work begins with a lemma on a special discrete-time stochastic system for which almost all of its sample paths starting from a nonzero initial value will never reach the origin subsequently. This motivates us to deal with the asymptotic stability in probability of discrete-time stochastic systems. A stochastic Lyapunov theorem on asymptotic stability in probability is proved by means of the convergence theorem of supermartingale. An example is given to show the difference between asymptotic stability in probability and almost surely asymptotic stability. Based on the stochastic Lyapunov theorem, the problem of asymptotic stabilization for discrete-time stochastic control systems is considered. Some sufficient conditions are proposed and applied for constructing asymptotically stable feedback controllers. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we propose a stochastic scheduling strategy for estimating the states of N discrete-time linear time invariant (DTLTI) dynamic systems, where only one system can be observed by the sensor at each time instant due to practical resource constraints. The idea of our stochastic strategy is that a system is randomly selected for observation at each time instant according to a pre-assigned probability distribution. We aim to find the optimal pre-assigned probability in order to minimize the maximal estimate error covariance among dynamic systems. We first show that under mild conditions, the stochastic scheduling problem gives an upper bound on the performance of the optimal sensor selection problem, notoriously difficult to solve. We next relax the stochastic scheduling problem into a tractable suboptimal quasi-convex form. We then show that the new problem can be decomposed into coupled small convex optimization problems, and it can be solved in a distributed fashion. Finally, for scheduling implementation, we propose centralized and distributed deterministic scheduling strategies based on the optimal stochastic solution and provide simulation examples. [ABSTRACT FROM AUTHOR]

The mathematical modeling of neuronal signals is a relevant problem in neuroscience. The complexity of the neuron behavior, however, makes this problem a particularly difficult task. Here, we propose a discrete-time linear time-invariant (LTI) model with a rational function in order to represent the neuronal spike detected by an electrode located in the surroundings of the nerve cell. The model is presented as a cascade association of two subsystems: one that generates an action potential from an input stimulus, and one that represents the medium between the cell and the electrode. The suggested approach employs system identification and signal processing concepts, and is dissociated from any considerations about the biophysical processes of the neuronal cell, providing a low-complexity alternative to model the neuronal spike. The model is validated by using in vivo experimental readings of intracellular and extracellular signals. A computational simulation of the model is presented in order to assess its proximity to the neuronal signal and to observe the variability of the estimated parameters. The implications of the results are discussed in the context of spike sorting. [ABSTRACT FROM AUTHOR]

This work proposes a new approach to the blind inversion of Wiener systems. A Wiener system is composed of a linear time-invariant (LTI) sub-system followed by a memoryless nonlinear function. The goal is to recover the input signal by knowing just the output of the Wiener system, and the straightforward scheme to achieve this is called the Hammerstein system – apply a memoryless nonlinear mapping followed by a LTI sub-system to the output signal of the Wiener system. If the input of the Wiener system is originally iid and some mild conditions are satisfied, the inversion is possible. Based on this statement and the limitations of relevant previous works, a solution is proposed combining (i) immune-inspired optimization algorithms, (ii) information theory and (iii) IIR filters that yield a robust scheme with a relatively reduced risk of local convergence. Experimental results indicated a similar or superior performance of the new approach, in comparison with two other blind methodologies. [ABSTRACT FROM AUTHOR]

This paper shows that the adaptive output error identifier for linear time-invariant continuous-time systems proposed by Bestser and Zeheb is robust vis-à-vis finite energy measurement noise. More precisely, it is proven that the map from the noise to the estimation error is [ABSTRACT FROM AUTHOR]

It is known that the Common Algorithmic Problem (CAP) has the nice property that several other NP-complete problems can be reduced to it in linear time. The decision version of this problem is known to be efficiently solved by a family of recognizer P systems with active membranes with three electrical charges working in the maximally parallel way. We here work with a variant of P systems with active membranes without polarizations and present a uniform solution to CAP in the minimally parallel mode. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of static output feedback (SOF) stabilization for discrete-time LTI systems. We approach this problem using the recently developed periodically time-varying memory state-feedback controller (PTVMSFC) design scheme. A bilinear matrix inequality (BMI) condition which uses a pre-designed PTVMSFC is developed to design the periodically time-varying memory SOF controller (PTVMSOFC). The BMI condition can be solved by using BMI solvers. Alternatively, we can apply two-steps and iterative linear matrix inequality algorithms that alternate between the PTVMSFC and PTVMSOFC designs. Finally, an example is given to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

Let T be a tree on a set V of nodes. The p- th power T of T is the graph on V such that any two nodes u and w of V are adjacent in T if and only if the distance of u and w in T is at most p. Given an n-node m-edge graph G and a positive integer p, the p- th tree root problem asks for a tree T, if any, such that G= T. Given an n-node m-edge graph G, the tree root problem asks for a positive integer p and a tree T, if any, such that G= T. Kearney and Corneil gave the best previously known algorithms for both problems. Their algorithm for the former (respectively, latter) problem runs in O( n) (respectively, O( n)) time. In this paper, we give O( n+ m)-time algorithms for both problems. [ABSTRACT FROM AUTHOR]

This paper investigates the semiglobal synchronization problem for a group of agents with input saturation under directed interaction topology, where each agent is modeled as a generic linear system rather than the single-integrator or double-integrator dynamics. The main result is the construction of a feedback coupling gain that achieves semiglobal synchronization if all the agents have identically saturated linear dynamics, which can be of any order. It is shown that the coupling gain obtained via parametric Lyapunov equations can semiglobally synchronize any directed network provided that the interaction topology has a directed spanning tree. Furthermore, due to the use of parametric Lyapunov equations, a convergence rate is analytically obtained. Finally, a simulation example is provided to demonstrate the effectiveness and advantages of our theoretical findings. [ABSTRACT FROM AUTHOR]

We generalize the important paper of Napp et al. (Automatica 47, 2373-2382, ), to discrete time-autonomous (ta) (=time-relevant), but not necessarily square-autonomous behaviors in arbitrary dimensions. This paper and therefore also the present one were essentially influenced by the papers of Wood et al. (SIAM J Control Optim 43, 1493-1520 ), and Willems (Proceedings of the International Conference on Multidimensional (nD) Systems, Aveiro, ). In the present paper the discrete domain of the independent variables is the lattice of vectors of integers of arbitrary (but fixed) length whose first component is a natural number and interpreted as a discrete time instant. The stability of an autonomous behavior is defined by a spectral condition on its characteristic variety. The behavior is time autonomous if each trajectory is determined by a fixed number of its initial values. Under a weak additional condition, a discrete stable and time-autonomous behavior is asymptotically stable in the sense that under suitable initial conditions its trajectories converge to zero when the time tends to infinity. We derive algorithms for the constructive verification of the assumptions of most of our results and in particular establish a constructive normal form of ta behaviors in arbitrary dimensions. The Fourier transform on finitely generated free abelian groups plays an important part in the derivations as it already did in the quoted papers. Stability and stabilization of multidimensional discrete behaviors were previously discussed by various colleagues, for instance by Bisiacco, Bose, Fornasini, Lin, Marchesini, Pillai, Quadrat, Rogers, Shankar, Sule, Valcher, Wood, but only partly from the analytic point of view. [ABSTRACT FROM AUTHOR]

This study investigates a separation principle for the H2 control of time-delay systems with partial observations. The authors first consider the linear quadratic regulation problem for time-delay systems. Based on the dynamic programming technique, the solution to the controller is given in terms of a backward partial difference Riccati equation. Then the estimation problem is investigated for linear discrete-time systems in the presence of time-delays. By employing the innovation analysis approach, the linear minimum-mean-square error (LMMSE) estimator is developed in terms of a forward partial difference Riccati equation. The Riccati equation is of the same dimension as the plant. Therefore compared with the conventional augmented approach, the presented approach greatly lessens the computational demand when the delay is large. Finally, they show that the separation principle holds in the following sense: an optimal controller can be obtained from two parts, one associated with the optimal control problem when state variable is available, and the other one associated with the LMMSE estimation problem. [ABSTRACT FROM AUTHOR]

Long-term survivors in trials with survival endpoints are subjects who will not experience the event of interest. Membership in the class of long-term survivors is unobserved and should be inferred from the data by means of a mixture model. An important question is how large the sample size should be to come to accurate conclusions with respect to the effect of treatment. This question is studied for trials with survival endpoints in discrete time by means of a simulation study. Various combinations of sample size, hazard probability, and probability of being a long-term survivor are studied. The results show that hazard probability has a large effect on the accuracy of the treatment effect estimate. A sample size of 200 might be sufficient for large hazard probabilities, whereas large sample sizes of 5,000 cases should be considered for small hazard probabilities. [ABSTRACT FROM PUBLISHER]

We deal with the finite-time control problem for discrete-time Markov jump systems subject to saturating actuators. A finite-state Markovian process is given to govern the transition of the jumping parameters. A controller designed for unconstrained systems combined with a dynamic antiwindup compensator is given to guarantee that the resulting system is mean-square locally asymptotically finite-time stabilizable. The proposed conditions allow us to find dynamic anti-windup compensator which stabilize the closed-loop systems in the finite-time sense. All these conditions can be expressed in the form of linear matrix inequalities and therefore are numerically tractable, as shown in the example included in the paper. [ABSTRACT FROM AUTHOR]

Abstract: This paper concerns the stabilization of discrete-time two-input two-output (TITO) linear time-invariant (LTI) systems over communication channels. We consider parallel additive white noise (AWN) channels, in which each individual channel is independently constrained in the signal-to-noise ratio (SNR). Necessary and sufficient conditions for stabilizability are obtained on the SNRs of the channels for both state and output feedback architectures. Our main results are derived assuming that the channel is located between the controller and the plant. We also consider stabilizability when the channel is between the plant and the controller, showing that there exists a duality between the results for both architectures. [Copyright &y& Elsevier]

This study investigates the optimal tracking performance of multiple-input multiple-output linear time-invariant systems over a noisy channel in the feedback path. The communication channel is also subject to data dropouts, which was modelled as a binary stochastic process. The problem under consideration amounts to determining the minimal error in tracking a Brownian motion random process, which emulates a step reference signal in the deterministic setting. With the unity feedback and two-parameter control structure, a lower bound and an exact expression of optimal tracking performance are obtained respectively. It is shown how the noise may degenerate the tracking performance and how the data dropouts effect may intertwine with unstable poles and non-minimum phase zeros, including the location and direction, which are intrinsic characteristics of the plant. Finally, computer simulations are provided to illustrate the analytical results obtained. [ABSTRACT FROM AUTHOR]

The paper deals with creating an indoor power line model based on random parameters. This model approximates the real parameters of the power line communication with sufficient precision. A detailed analysis of earlier and current research in power line communication modelling, especially for power line models, is described. Measurement of transmission line parameters and power line model verification follows. Based on model analysis and load impedance measurement, a mathematical description of the model is designed. A reference model for different scenarios is realized too. The last part gives the analysis of this model and simulation results. [ABSTRACT FROM AUTHOR]

Abstract: We introduce the family of limited model information control design methods, which construct controllers by accessing the plant’s model in a constrained way, according to a given design graph. We investigate the closed-loop performance achievable by such control design methods for fully-actuated discrete-time linear time-invariant systems, under a separable quadratic cost. We restrict our study to control design methods which produce structured static state feedback controllers, where each subcontroller can at least access the state measurements of those subsystems that affect its corresponding subsystem. We compute the optimal control design strategy (in terms of the competitive ratio and domination metrics) when the control designer has access to the local model information and the global interconnection structure of the plant-to-be-controlled. Finally, we study the trade-off between the amount of model information exploited by a control design method and the best closed-loop performance (in terms of the competitive ratio) of controllers it can produce. [Copyright &y& Elsevier]

Abstract: This paper presents a systematic study on the properties of blocked linear systems that have resulted from blocking discrete-time linear time invariant systems. The main idea is to explore the relationship between the blocked and the unblocked systems. Existing results are reviewed and a number of important new results are derived. Focus is given particularly on the zero properties of the blocked system as no such study has been found in the literature. [Copyright &y& Elsevier]

Abstract: In this paper a controller reduction method for discrete-time linear time-invariant systems is described. Using the bounded-real lemma, the proposed method generates reduced controllers with closed loop stability and norm performance guarantee. Information of the full controller is used as a basis for reduction using singular value decomposition. This is different from traditional model reduction schemes such as weighted balanced truncation. Numerical assessment of the proposed method is given in the end of the paper. [Copyright &y& Elsevier]