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In this paper, it is shown that, under some mild assumptions, it is possible to design observers for linear time-invariant continuous-time and discrete-time systems by feeding classical linear observers (e.g., the Kalman filters and the Luenberger observer) with the successive integrals and the moving average of the measured output, respectively. The main interest in these observers relies on the fact that both the integral and the moving average exhibit low-pass behaviors, thus allowing the design of observers that are less sensitive to high-frequency noise. Examples are reported all throughout this paper to corroborate the theoretical results and to highlight the improved filtering properties of the proposed observers. [ABSTRACT FROM AUTHOR]

We motivate the need for a new notion of observability for systems over finite alphabets and propose three new notions of output observability, thereby shifting our attention to the problem of state estimation for output prediction. We then consider a class of systems over finite alphabets with linear internal dynamics, finite-valued control inputs, and finitely quantized outputs. We derive a set of sufficient conditions and a set of necessary conditions for these systems to be output observable, propose an algorithmic procedure to verify one of these conditions, and construct finite memory output observers when certain conditions are met. [ABSTRACT FROM AUTHOR]

This note is concerned with asymptotic stability analysis of discrete-time linear time-varying (DLTV) systems. The contribution can be summarized as follows. First, the difference between nonuniformly exponential stability (ES), which was not well recognized in the literature, and uniformly ES (UES) was revealed and illustrated by numerical examples. Second, some state transition matrices and difference Lyapunov inequalities (DLIs) based necessary and sufficient conditions were derived for testing different stability concepts including asymptotic stability (AS), ES, and UES of general DLTV systems. The main feature of the DLIs-based criteria is that the time-difference of the Lyapunov function is not required to be negative definite. Finally, the ES concept was utilized for analysis stability of a class of upper triangular DLTV systems and perturbated DLTV systems. The effectiveness of the proposed results was demonstrated by some examples. [ABSTRACT FROM AUTHOR]

Estimating disturbances/unknown inputs of a given system is an important technique that finds various engineering and industrial applications. Two such examples are the so-called disturbance-observer-based control and fault detection/isolation. The traditional design of a disturbance/unknown input observer (DOB/UIOB) usually involves utilizing the inverse of the model of the open-loop system. Hence, such design can only be applied to systems with stable, or “minimal phase”, zeros. In this manuscript, we propose a novel adaptive observer for estimating the unknown and nearly periodic input of a linear-time-invariant (LTI) single-input-single-output (SISO) discrete-time system. The observer assumes the form of an adaptive FIR filter whose coefficients are obtained based on the given system model via the least-squares algorithm with the covariance matrix reset. An important advantage of the proposed approach is that the approach does not involve inverting the open-loop system model; therefore, it can be successfully applied to both minimum-phase and non-minimum phase systems. The effectiveness of the proposed observer design is assessed by a numerical example. [ABSTRACT FROM AUTHOR]

Optimal input design for parameter estimation has obtained extensive coverage in the past. A key problem here is that the optimal input depends on some unknown system parameters that are to be identified. Adaptive design is one of the fundamental routes to handle this problem. Although there exist a rich collection of results on this problem, there are few results that address dynamical systems. This paper presents sufficient conditions for convergence/consistency and asymptotic optimality for a class of adaptive systems consisting of a recursive prediction error estimator and an input generator depending on the time-varying parameter estimates. The results apply to a general family of single input single output linear time-invariant systems. An important application is adaptive input design for which the results imply that, asymptotically in the sample size, the adaptive scheme recovers the same accuracy as the off-line prediction error method that uses data from an experiment where perfect knowledge of the system has been used to design an optimal input spectrum. [ABSTRACT FROM PUBLISHER]

We consider the problem of stabilizing a continuous-time linear time-invariant system subject to communication constraints. A noiseless finite-capacity communication channel connects the process sensors to the controller/actuator. The sensor's state measurements are encoded into symbols from a finite alphabet, transmitted through the channel, and decoded at the controller/actuator. We suppose that the transmission of each symbol costs one unit of communication resources, except for one special symbol in the alphabet that is “free” and effectively signals the absence of transmission. We explore the relationship between the encoder's average bit-rate, its average consumption of communication resources, and the ability of the controller and encoder/decoder pair to stabilize the process. We present a necessary and sufficient condition for the existence of a stabilizing controller and encoder/decoder pair, which depends on the encoder's average bit-rate, its average resource consumption, and the unstable eigenvalues of the process. Moreover, if this condition is satisfied, a stabilizing encoding scheme can be constructed that consumes resources at an arbitrarily small rate, provided the encoder has access to a sufficiently precise clock or large memory. The paper concludes with the analysis of a simple emulation-based controller and event-based encoder/decoder pair that are easy to implement, stabilize the process, and have average bit-rate and resource consumption within a constant factor of the optimal bound. [ABSTRACT FROM PUBLISHER]

This technical note presents a feedback design approach to minimise state ultimate-bounds (UBs) in linear time-invariant discrete-time systems subject to non-vanishing bounded disturbances. A target closed-loop eigenstructure is first constructed to achieve the lowest possible UBs for one or more state components of the system. Structural conditions on the system matrices are then derived to guarantee that the target eigenstructure can be assigned by state feedback. When the required structural conditions are satisfied, an eigenvector assignment procedure can be applied to simultaneously minimise multiple UBs in systems with multiple inputs. The results are illustrated by a numerical example drawn from a distributed voltage control problem in inverter-based microgrids. [ABSTRACT FROM PUBLISHER]

We present and examine a novel method for obtaining solutions to specific discrete-time optimal control problems. Our approach is based on linear state dynamics and convexity assumptions commonly satisfied in practical applications. We show that the important class of optimal switching problems under partial observation is covered by our methodology, and we exploit specific model features to achieve simple algorithmic form of a numerical solution. [ABSTRACT FROM AUTHOR]

The stability of linear threshold dynamic neural networks is studied, and a series of methods to obtain globally attractive sets is proposed. A sufficient condition to judge whether an invariant set is a globally attractive set is also proposed. This method requires only the solution to a class of linear matrix inequalities. Also, two direct methods to obtain globally attractive sets are given. The stability criteria presented are based on the proposed globally attractive sets. Some numerical examples are given to illustrate the effectiveness of the obtained results. [ABSTRACT FROM PUBLISHER]

We investigate the control of constrained stochastic linear systems when faced with limited information regarding the disturbance process, i.e., when only the first two moments of the disturbance distribution are known. We consider two types of distributionally robust constraints. In the first case, we require that the constraints hold with a given probability for all disturbance distributions sharing the known moments. These constraints are commonly referred to as distributionally robust chance constraints. In the second case, we impose conditional value-at-risk (CVaR) constraints to bound the expected constraint violation for all disturbance distributions consistent with the given moment information. Such constraints are referred to as distributionally robust CVaR constraints with second-order moment specifications. We propose a method for designing linear controllers for systems with such constraints that is both computationally tractable and practically meaningful for both finite and infinite horizon problems. We prove in the infinite horizon case that our design procedure produces the globally optimal linear output feedback controller for distributionally robust CVaR and chance constrained problems. The proposed methods are illustrated for a wind blade control design case study for which distributionally robust constraints constitute sensible design objectives. [ABSTRACT FROM PUBLISHER]

We present necessary and sufficient conditions for stabilizing a discrete-time LTI plant in the mean squared sense when a sensor transmits the plant state information to a remotely placed controller across a Gaussian product channel. The Gaussian product channel models a continuous-time waveform Gaussian channel, where the encoder transmits information to the receiver across multiple noisy paths. The conditions presented are in terms of the power at the transmitter, noise variances and the unstable eigenvalues of the plant. It is known that linear coding schemes may lead to overly restrictive stabilizability conditions in such scenarios. We present a nonlinear coding scheme and present the resulting sufficient stabilizability conditions. We then prove the necessity of the conditions using information theoretic tools. [ABSTRACT FROM PUBLISHER]

Subspace-based methods have been effectively used to estimate multi-input/multi-output, discrete-time, linear-time invariant systems from uniformly spaced spectrum samples. A critical step in these methods is the splitting of causal and noncausal invariant subspaces of a Hankel matrix built from spectrum measurements via singular-value decomposition in order to determine model order. Quite often, in particular when signal-to-noise ratio is low, unmodelled dynamics is present, and the number of measurements is small, this step is inconclusive since the assumed mirror image symmetry with respect to the unit circle between the eigenvalues of the invariant spaces is lost. In this paper, we propose a new model order selection and invariant space splitting scheme based on the regularized nuclear norm optimization in combination with a particular subspace method that is insensitive to noise and undermodelling. By a detailed numerical study, efficacy of the proposed scheme is shown for a broad range of signal-to-noise ratio and short data records. [ABSTRACT FROM AUTHOR]

This technical note deals with the state feedback H\infty control problem for linear time-invariant discrete-time singular systems. Relied on the use of auxiliary matrices and a positive scalar, a novel necessary and sufficient condition for the bounded real lemma is derived for discrete-time singular systems. The characterization is reduced to a strict linear matrix inequality (LMI) when the scalar is fixed, and the resulting LMI is non-conservative as long as the scalar is chosen sufficiently large. Moreover, the result is further expanded to H\infty controller design, and a numerically efficient and reliable design procedure is given. Since no particular restriction is imposed on the auxiliary matrices, the proposed result outperforms the existing methods in the literature. Numerical examples are included to illustrate the effectiveness of the present result. [ABSTRACT FROM AUTHOR]

Matrosov's relaxation of Lyapunov conditions for uniform global asymptotic stability in time-varying systems is extended to stochastic, set-valued discrete-time systems. Nested Matrosov functions are used to give conditions for stability that complement invariance principles for time-invariant systems. Unlike invariance principles, Matrosov functions also can be applied to general time-varying systems. [ABSTRACT FROM AUTHOR]

In this note, an approach based on lifting is introduced for the observer based fault detection (FD) of linear discrete-time periodic systems. The main contribution of this note is to give an analytic expression to transform the linear time-invariant (LTI) observer based residual generator designed based on the lifted LTI reformulation of the periodic system into a periodic observer based residual generator to reduce detection delay. The result enables a systematic transfer of the existing observer based FD methods for discrete LTI systems to discrete-time periodic systems. [ABSTRACT FROM AUTHOR]

Consider a first order linear time-invariant discrete time system driven by process noise, a pre-processor that accepts causal measurements of the state of the system, and a state estimator. The pre-processor and the state estimator are not co-located, and, at every time-step, the pre-processor transmits either a real number or a free symbol to the estimator. We seek the pre-processor and the estimator that jointly minimize a cost that combines two terms; the expected squared state estimation error and a communication cost. In our formulation, the transmission of a real number from the pre-processor to the estimator incurs a positive cost while free symbols induce zero cost. This paper proves analytically that a symmetric threshold policy at the pre-processor and a Kalman-like filter at the estimator, which updates its estimate linearly in the presence of free symbols, are jointly optimal for our problem. [ABSTRACT FROM AUTHOR]

We characterize a family of parametrized robust control invariant sets for linear discrete time systems subject to additive but bounded state disturbances. The existence of a member of the introduced family of parametrized robust control invariant sets can be verified by solving a tractable convex optimization problem in the linear convex case, which reduces to the standard linear or convex quadratic programme in the linear polytopic case. The developed method can also be utilized to detect and obtain an implicit representation of local control Lyapunov functions in the linear convex case from the solution of a single and tractable convex optimization problem. The offered method permits for the computation of polytopic robust control invariant sets and local control Lyapunov functions of indirectly controlled and limited complexity in the linear polytopic case. [ABSTRACT FROM AUTHOR]

In this technical note, the relation between notions of uniform observability of discrete-time nonlinear systems based on injectivity of an observation map (window), the full-rankness of its Jacobian, and a K-function is investigated. It is proven that a system is uniformly observable in the sense of injectivity of the observation map (together with the full-rankness of its Jacobian) if and only if it is so in some K-function senses. [ABSTRACT FROM AUTHOR]

This note addresses the stability problem of continuous-time positive systems with time-varying delays. It is shown that such a system is asymptotically stable for any continuous and bounded delay if and only if the sum of all the system matrices is a Hurwitz matrix. The result is a time-varying version of the widely-known asymptotic stability criterion for constant-delay positive systems. A numerical example illustrates the correctness of our result. [ABSTRACT FROM AUTHOR]

The note deals with the finite-time analysis and design problems for continuous-time, time-varying linear systems. Necessary and sufficient conditions and a sufficient condition for finite-time stability are devised. Moreover, sufficient conditions for the solvability of both the state and the output feedback problems are stated. Such results require the feasibility of optimization problems involving Differential Linear Matrix Inequalities. Some numerical examples illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this note, necessary and sufficient numerical conditions for asymptotic stability and for uniform asymptotic stability of linear continuous time-varying systems are derived. For a given set of initial conditions, a tube containing all the trajectories of the system is constructed in the state space. At each instant of time, there exists an initial condition inside the set such that the resulting trajectory attains the border of the tube. Based on the above formulation, necessary and sufficient conditions for asymptotic stability and for uniform asymptotic stability are expressed through the solution of a linear differential Lyapunov equation. The conditions can deal with the stability of periodic systems as well. One of the main characteristics of the proposed necessary and sufficient conditions is that the only assumption on the dynamical matrix of the time-varying system is continuity. Examples from the literature illustrate the superiority of the proposed conditions when compared to other methods. [ABSTRACT FROM AUTHOR]

The purpose of this note is to consider the quadratic stabilization of LPV systems in the realistic case where only Gaussian noisy parameter measures are available. Though neglected in the actual literature on LPV systems, this question is particular important because in all situations of a practical interest the parameter measurements (or estimates) are never exact. The assumed noisy nature of physical parameter readings requires a specifically developed approach consisting of mixed robust and LPV control methods. In the present case, an approach based on a vertex result on interval time varying (ITV) matrices is proposed. This allows the solvability conditions to be stated in terms of a set of LMI's, whose number is independent of the number of time-varying parameters. [ABSTRACT FROM AUTHOR]

This paper proposes a new control parametrization under the model predictive control (MPC) framework for constrained linear discrete-time systems with bounded disturbances. The proposed parametrization takes the form of a special piecewise affine disturbance feedback in an effort to reduce conservatism. It is a generalization of linear disturbance feedback parametrization, introduced in the recent literature. Numerical computations and stability properties of the resulting MPC problem using the proposed parametrization are discussed. When the disturbance set and the problem data satisfy mild assumptions, the associated finite-horizon optimization can be computed efficiently and exactly. The advantage of the proposed parametrization over linear disturbance feedback is illustrated via numerical examples. [ABSTRACT FROM AUTHOR]

In this technical note, exact and approximate solutions of the discrete-time suboptimal proportional-integral-H∞-estimation problem for affine nonlinear systems using finite-dimensional estimators (filters) are presented. Sufficient conditions for the solvability of the problem are given in terms of discrete-time Hamilton-Jacobi-Isaac's equations. For linear systems, it is shown that, these equations reduce to a system of linear-matrix inequalities. Simulation results are also presented to show the benefit of the new approach. [ABSTRACT FROM AUTHOR]

A weak concept of sampled-data feedback stabilization for the case of autonomous systems is presented and its Lyapunov characterization is established. Sufficient conditions are derived for the existence of a timevarying sampled-data feedback exhibiting global stabilization for certain class of nonlinear systems. [ABSTRACT FROM AUTHOR]

An exact method is presented for discretizing a constant-coefficient, non-square, matrix differential Riccati equation, whose solution is assumed to exist. The resulting discrete-time equation gives the values that have no error at discrete-time instants for any discrete-time interval. The method is based on a matrix fractional transformation, which is more general than existing ones, for linearizing the differential Riccati equation. A numerical example is presented to compare the proposed method with that based on gage invariance and bilinearization, which has better performances than the conventional forward-difference method. [ABSTRACT FROM AUTHOR]

This paper addresses robust performance analysis problems of linear time-invariant (LTI) systems affected by real parametric uncertainties. These problems, known also as a special class of structured singular value computation problems, are inherently intractable (NP-hard problems). As such intensive research effort has been made to obtain computationally tractable and less conservative analysis conditions, when linear matrix inequality (LMI) plays an important. Nevertheless, since LMI-based conditions are expected to be conservative in general, it is often the case that we cannot conclude anything if the LMI at hand turns out to be infeasible. This motivates us to consider the dual of the LMI and examine the structure of the dual solution. By pursuing this direction, in this paper, we provide rank conditions on the dual solution matrix under which we can conclude that the underlying robust performance is never attained. In particular, a set of uncertain parameters that violates the specified performance can be computed. These results come from block-moment mate is structure of the dual variable, which is consistent with the recent results on polynomial optimization. This particular structure enables us to make good use of simultaneous diagonalizability property of commuting diagonalizable matrices so that the sound rank conditions fur the exactness verification can be obtained. [ABSTRACT FROM AUTHOR]

We investigate several fundamental aspects of the theory of linear distributed systems with spatially periodic coefficients. We develop a spatial-frequency domain representation analogous to the lifted or frequency response operator representation for linear time periodic systems. Using this representation, we introduce the notion of the H² norm for this class of systems and provide algorithms for its computation. A stochastic interpretation of the H² norm is given in terms of spatially cyclostationary random fields and spectral-correlation density operators. When the periodic coefficients are viewed as feedback modifications of spatially invariant systems, we show how they can stabilize or destabilize the original systems in a manner analogous to vibrational control or parametric resonance in time periodic systems. Two examples from physics are provided to illustrate the main results. [ABSTRACT FROM AUTHOR]

A necessary and sufficient condition for decentralized control of discrete event systems via prioritized composition with exclusion (PCX) is provided. PCX was extended from prioritized synchronous composition (PSC) in order to model various Boolean modes of decision fusion by allowing the exclusivity of participation in system interactions [1]. A notion of PCX-coobservability is introduced that captures the nature of PCX-based decision fusion, and a testing algorithm with polynomial complexity in the states of plant and specification is presented. The result is extended for multiple supervisors with multiple exclusivity sets based on an extended PCX definition. [ABSTRACT FROM AUTHOR]

In conservative (or complete) trace-based distributed fault diagnosis it is common to compute, for each component, a preliminary local estimate consisting of all possible traces that can generate the same local symptom (i.e., a collection of sequences of observable events) as the one being received from that component up to a specific time instant. Then communication among local trace estimators can be used to refine those preliminary local estimates. An approach has been proposed by Su and Wonham to perform such refinement in terms of achieving global or local consistency among local estimates. But that approach does not consider timing mismatch and channel distortion in the process of collecting local symptoms, which may result in incorrect estimates in practical applications. In this paper, we will provide a new approach to handle trace estimation under timing mismatch and channel distortion. [ABSTRACT FROM AUTHOR]

This study employs the free-weighting matrix approach to investigate the output feedback control of a linear discrete-time system with an interval time-varying delay. First, the delay-dependent stability is analyzed using a new method of estimating the upper bound on the difference of a Lyapunov function without ignoring any terms; and based on the results, a design criterion for a static output feedback (SOF) controller is derived. Since the conditions thus obtained for the existence of admissible controllers are not expressed strictly in terms of linear matrix inequalities, a modified cone complementarity linearization algorithm is employed to solve the nonconvex feasibility SOF control problem. Furthermore, the problem of designing a dynamic output feedback controller is formulated as one of designing an SOF controller. Numerical examples demonstrate the effectiveness of the method and its advantage over existing methods. [ABSTRACT FROM AUTHOR]

This work proposes a technique for the design of stabilizing dynamic output feedback controllers for discrete-time linear systems with rate and amplitude saturating actuators. The nonlinear effects introduced by the saturations in the closed-loop system are taken into account by using a generalized sector condition, which leads to theoretical conditions for solving the problem directly in the form of linear matrix inequalities. [ABSTRACT FROM AUTHOR]

Absfract-In this paper, the H∞ filtering problem is investigated for a general class of nonlinear discrete-time stochastic systems with missing measurements. The system under study is not only corrupted by state-dependent white noises but also disturbed by exogenous inputs. The measurement output contains randomly missing data that is modeled by a Bernoulli distributed white sequence with a known conditional probability. A filter of very general form is first designed such that the filtering process is stochastically stable and the filtering error satisfies H∞ performance constraint for all admissible missing observations and nonzero exogenous disturbances under the zero-initial condition. The existence conditions of the desired filter are described in terms of a second-order nonlinear inequality. Such an inequality can be decoupled into some auxiliary ones that can be solved independently by taking special form of the Lyapunov functionals. As a consequence, a linear time-invariant filter design problem is discussed for the benefit of practical applications, and some simplified conditions are obtained. Finally, two numerical simulation examples are given to illustrate the main results of this paper. [ABSTRACT FROM AUTHOR]

Abstract-The paper deals with definitions of zeros and poles and their features in finite-dimensional linear continuous-time periodic (FDLCP) systems under a harmonic framework. More precisely, system and transfer zeros and poles in the harmonic wave-to-wave sense are defined on what we call the regularized harmonic system operators and the harmonic transfer operators of FDLCP systems by means of regularized determinants; then their composition and properties related to system structures are examined via the Floquet theory and controllability/observability decompositions of FDLCP systems. The study shows that under mild assumptions, the harmonic transfer operators of FDLCP systems are analytic and meromorphic, on which zeros and poles are well-defined. Basic zero/pole relationships are established, which are similar to their linear time-invariant counterparts and in particular explicate some interesting harmonic wave-to-wave behaviors of FDLCP systems. The results are significant in analysis and synthesis of FDLCP systems when the harmonic approach is adopted. [ABSTRACT FROM AUTHOR]

This note considers the design of transmission control protocol (TCP)-like congestion control protocols for deployment in high-speed communication networks. A basic problem in this area is to design congestion control strategies that probe more aggressively than standard TCP, but which coexist with each other and result in globally stable and equitable network behavior. In this note, we take a first step towards this goal, by formulating the TCP dynamics as a discrete linear system with nonlinear feedback gain. Under the assumption of player synchronisation, conditions for global network stability are derived in the form of growth bounds on the local nonlinear probing functions. [ABSTRACT FROM AUTHOR]

A periodic adaptive control approach is proposed for a class of nonlinear discrete-time systems with time-varying parametric uncertainties that are periodic, and the only prior knowledge is the periodicity. The new adaptive controller updates the parameters and the control signal periodically in a point-wise manner over one entire period, and in the sequel, achieves the asymptotic tracking convergence. The result is further extended to a scenario with mixed time-varying and time-invariant parameters, and a hybrid classical and a periodic adaptation law is proposed to handle the scenario more appropriately. The extension of the periodic adaptation to systems with unknown input gain, higher order dynamics, and tracking problems is also discussed. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stabilization of discrete-time linear systems with quantization of the input and output spaces, i.e., when available values of inputs and outputs are discrete. Unlike most of the existing literature, we assume that how the input and output spaces are quantized is a datum of the problem, rather than a degree of freedom in design. Our focus is hence on the existence and synthesis of symbolic feedback controllers, mapping output words into the input alphabet, to steer a quantized I/O system to within small invariant neighborhoods of the equilibrium starting from large attraction basins. We provide a detailed analysis of the practical stabilizability of systems in terms of the size of hypercubes bounding the initial conditions, the state transient, and the steady-state evolution. We also provide an explicit construction of a practically stabilizing controller for the quantized I/O case. [ABSTRACT FROM AUTHOR]

We are concerned with the output norm-constrained infinite-horizon linear quadratic regulation problem, where the underlying state-control constraints are specified by curved, rather than polyhedral, surfaces. Each suboptimal problem admits an exact convex synthesis condition expressed by an increasing union of linear matrix inequalities and results in an eventually time-invariant controller satisfying the desired performance level subject to given constraints and closed-loop stability. The output norm-constrained minimum-time control problem is also dealt with as a corollary. [ABSTRACT FROM AUTHOR]

Linear, state-delayed, continuous-time systems with stochastic uncertainties in their state-space model are considered. The problems of both H∞ state-feedback control and filtering are solved, for the stationary case, via an input-output approach by which the system is replaced by a nonretarded system with deterministic norm-bounded uncertainties. In both problems, a cost function is defined that is the expected value of the standard H∞ performance index with respect to the uncertain parameters. Three examples are given that demonstrate the applicability of the theory. [ABSTRACT FROM AUTHOR]

This paper investigates the stabilizability of uncertain linear time-invariant (LTI) systems via structurally constrained controllers. First, an LTI uncertain system is considered whose state-space matrices depend polynomially on the uncertainty vector, defined over some region. It is shown that if the system is stabilizable by a structurally constrained controller in one point belonging to the region, then it is stabilizable by a controller with the same structure in all points belonging to the region, except for those located on an algebraic variety. Thus, if a system is stabilizable via a constrained controller at the nominal point, then it is almost always stabilizable at any operating point around the nominal model. It is also shown how this algebraic variety (or the dominant subvariety of it) can be computed efficiently. The results obtained in this paper encompass a broad range of the existing results in the literature on robust stability of the LTI systems, in addition to new ones. [ABSTRACT FROM AUTHOR]

This note investigates the robust stability of uncertain linear time-invariant systems in polytopic domains by means of parameter-dependent linear matrix inequality (PD-LMI) conditions, exploiting some algebraic properties provided by the uncertainty representation. A systematic procedure to construct a family of finite-dimensional LMI relaxations is provided. The robust stability is assessed by means of the existence of a Lyapunov function, more specifically, a homogeneous polynomially parameter-dependent Lyapunov (HPPDL) function of arbitrary degree. For a given degree g, if an HPPDL solution exists, a sequence of relaxations based on real algebraic properties provides sufficient LMI conditions of increasing precision and constant number of decision variables for the existence of an HPPDL function which tend to the necessity. Alternatively, if an HPPDL solution of degree g exists, a sequence of relaxations which increases the number of variables and the number of LMIs will provide an HPPDL solution of larger degree. The method proposed can be applied to determine homogeneous parameter-dependent matrix solutions to a wide variety of PD-LMIs by transforming the infinite-dimensional LMI problem described in terms of uncertain parameters belonging to the unit simplex in a sequence of finite-dimensional LMI conditions which converges to the necessary conditions for the existence of a homogeneous polynomially parameter-dependent solution of arbitrary degree. Illustrative examples show the efficacy of the proposed conditions when compared with other methods from the literature. [ABSTRACT FROM AUTHOR]

This note deals with the problem of observer-based fast rate fault detection for a class of multirate sampled-data (MSD) systems. Applying a lifting technique, a linear time-invariant (LTI) representation with slow sampling period is firstly obtained for the MSD systems and, based on this, an observer-based fault detection filter is considered as a residual generator. Then an optimization fault detection approach for LTI systems is modified to the residual generation for the MSD systems and, by solving a discrete-time Algebraic Riccati equation, a family of optimal solutions with causality constraint can be obtained. An inverse lifting operation on the generated residual implements its fast rate. The residual evaluation problem is also considered. A numerical example is finally given to illustrate the effectiveness of the proposed design techniques. [ABSTRACT FROM AUTHOR]

Extremum seeking control (ESC) schemes based on numerical optimization are proposed in this paper. The extremum seeking problem is treated as an optimization with dynamic system constraints. The numerical optimization-based extremum seeking control scheme is first applied to lineat time-invariant (LTI) systems, then it is extended to a class of feedback linearizable systems. The convergence of the ESC scheme is guaranteed by the numerical optimization algorithm and state regulation. The robustness of line search methods and trust region methods is studied, which provides further flexibility for the design of robust extremum seeking controller. Simulation study of antilock braking systems (ABS) design via extremum seeking control is addressed. [ABSTRACT FROM AUTHOR]

This paper describes the computation of reach sets for discrete-time linear control systems with time-varying coefficients and ellipsoidal bounds on the controls and initial conditions. The algorithms construct external and internal ellipsoidal approximations that touch the reach set boundary from outside and from in- side. Recurrence relations describe the time evolution of these approximations. An essential part of the paper deals with singular discrete-time linear systems. [ABSTRACT FROM AUTHOR]

This paper studies the construction of observers for nonlinear time-varying discrete-time systems in a general context, where a certain function of the states must be estimated. Appropriate notions of robust complete observability are proposed, under which a constructive proof of existence of an observer is developed. Moreover, a ‘transitive observer property’ is proven, according to which a state observer can be generated as the series connection of two observers. The analysis and the results are developed in general normed linear spaces, to cover both finite-dimensional and infinite-dimensional systems. [ABSTRACT FROM AUTHOR]

In terminal sliding-mode control, the system slates are brought to the origin in finite time using the concept of sliding-mode control. Though the theory of terminal sliding mode is well studied for continuous time systems, a discrete-time terminal sliding mode concept has not been investigated. This note analyses the applicability of terminal sliding-mode control in the discrete-time framework and discusses the problems involved in the discretization of continuous-time terminal sliding mode. The note also suggests a method to approach the discrete-time terminal sliding-mode control problem. [ABSTRACT FROM AUTHOR]

Bode's sensitivity integral is a well-known formula that quantifies some of the limitations in feedback control for linear time-invariant systems. In this note, we show that there is a similar formula for linear time-periodic systems. The harmonic transfer function is used to prove the result. We use the notion of roll-off 2, which means that the first time-varying Markov parameter is equal to zero. It then follows that the harmonic transfer function is an analytic operator and a trace class operator. These facts are used to prove the result. [ABSTRACT FROM AUTHOR]

This note studies the problem of robust controllability of linear time invariant multiple-input-multiple-output systems with A being or A and B both being sign-invariant interval matrices. For controllability, sufficient conditions as well as necessary and sufficient conditions based on interval division method are presented. The note also provides a way to handle interval systems that are not sign-invariant in the A matrix. Some examples illustrate the results. [ABSTRACT FROM AUTHOR]

Although techniques for directly synthesising sampled-data (SD) compensation are available in the literature, feedback controller design is perhaps best understood in a purely continuous-time setting. As such, a feedback controller is often designed in the continuous-time domain and then discretized for digital implementation. It is important for the discretization step involved to yield an SD approximation which captures the essential features of the original controller from the perspective of closed-loop behavior. In this note, a gap metric framework is developed for studying the controller discretization problem for linear time-invariant (LTI) plants and controllers, Importantly, knowledge of a gap metric distance between an LTI controller and an SD approximation permits explicit characterization of the possible difference in closed-loop performance with any LTI plant for which the LTI controller is known to work well, accounting for intersample behavior. The central result of the new framework gives rise to an algorithm for computing a gap metric measure of the distance between an LU controller and a given discretization, and a technique for synthesising a SD approximation which is optimal with respect to this metric. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of model (in)validation of discrete time, causal, linear time-invariant (LTI) stable models subject to slowly linear time-varying structured uncertainty using frequency domain data corrupted by additive noise. It is well known that in the case of structured LTI uncertainty the problem is NP hard in the number of uncertainty blocks. The main contribution of this paper shows that, on the other hand, if one considers arbitrarily slowly time varying uncertainty and noise In £2, then tractable, convex necessary and sufficient conditions for (in)validation can be obtained. Additional results include a discussion of the case where the noise is characterized in terms of the £∞ norm. [ABSTRACT FROM AUTHOR]