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The problem of solving linear equations is considered as one of the fundamental problems commonly encountered in science and engineering. In this article, the complex-valued time-varying linear matrix equation (CVTV-LME) problem is investigated. Then, by employing a complex-valued, time-varying QR (CVTVQR) decomposition, the zeroing neural network (ZNN) method, equivalent transformations, Kronecker product, and vectorization techniques, we propose and study a CVTVQR decomposition-based linear matrix equation (CVTVQR-LME) model. In addition to the usage of the QR decomposition, the further advantage of the CVTVQR-LME model is reflected in the fact that it can handle a linear system with square or rectangular coefficient matrix in both the matrix and vector cases. Its efficacy in solving the CVTV-LME problems have been tested in a variety of numerical simulations as well as in two applications, one in robotic motion tracking and the other in angle-of-arrival localization. [ABSTRACT FROM AUTHOR]

We address the problem of synthesizing provably correct controllers for linear systems with reach-avoid specifications. Discrete abstraction-based controller synthesis techniques have been developed for linear and nonlinear systems with various types of specifications. However, these methods typically suffer from the state space explosion problem. Our solution decomposes the overall synthesis problem into two smaller, and more tractable problems: one synthesis problem for an open-loop controller, which can produce a reference trajectory, and a second for synthesizing a tracking controller, which can enforce the other trajectories to follow the reference trajectory. As a key building-block result, we show that, once a tracking controller is fixed, the reachable states from an initial neighborhood, subject to any disturbance, can be overapproximated by a sequence of ellipsoids, with shapes that are independent of the open-loop controller. Hence, the open-loop controller can be synthesized independently to meet the reach-avoid specification for an initial neighborhood. Moreover, we are able to reduce the problem of synthesizing open-loop controllers to satisfiability problems over quantifier-free linear real arithmetic. The number of linear constraints in the satisfiability problem is linear to the number of hyperplanes as the surfaces of the polytopic obstacles and goal sets. The overall synthesis algorithm, computes a tracking controller, and then iteratively covers the entire initial set to find open-loop controllers for initial neighborhoods. The algorithm is sound and, for a class of robust systems, is also complete. We implement this synthesis algorithm in a tool RealSyn ver 2.0 and use it on several benchmarks with up to 20 dimensions. Experiment results are very promising: RealSyn ver 2.0 can find controllers for most of the benchmarks in seconds. [ABSTRACT FROM AUTHOR]

In this note, we investigate the stabilization of discrete-time linear systems with an unknown time-varying delay. Existing literature on the stabilization of time-delay systems require some knowledge, such as an upper bound, of the delay. In this paper, by proposing a switched low-gain feedback control law, we are able to achieve asymptotic stabilization of the system without any knowledge of the delay. In addition, the proposed switched low-gain feedback law also significantly improves the closed-loop system performance in terms of overshoot and convergence speed in comparison with the traditional fixed gain design. Simulation study illustrates the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

We study a sampled-data implementation of linear controllers that depend on the output and its derivatives. First, we consider an LTI system of relative degree $r\geq 2$ that can be stabilized using $r-1$ output derivatives. Then, we consider PID control of a second-order system. In both cases, the Euler approximation is used for the derivatives giving rise to a delayed sampled-data controller. Given a derivative-dependent controller that stabilizes the system, we show how to choose the parameters of the delayed sampled-data controller that preserves the stability under fast enough sampling. The maximum sampling period is obtained from LMIs that are derived using Taylor's expansion of the delayed terms with the remainders compensated by appropriate Lyapunov–Krasovskii functionals. Finally, we introduce the event-triggering mechanism that may reduce the amount of sampled control signals used for stabilization. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive $H_\infty $ static output feedback (SOF) control problem for continuous-time linear systems with stochastic sensor failures. A multi-Markovian variable is introduced to denote the failure scaling factors for each sensor. Different from the existing results, the failure parameters are stochastically jumping and their bounds of are unknown. An adaptive reliable $H_\infty $ SOF control method is proposed, where the controller parameters are updated automatically to compensate for the failure effects on systems. A novel cubic absolute Lyapunov function is proposed to design adaptive laws only using measured output with sensor failures, and the convergence of jumping adaptive parameters is ensured by a trajectory initialization approach. The resultant designs can guarantee the asymptotic stability with an adaptive $H_\infty $ performance of closed-loop systems regardless of sensor failures. Finally, the simulation results on the “Raptor-90” helicopter are given to show the effectiveness of the proposed approaches. [ABSTRACT FROM PUBLISHER]

This paper studies the distributed optimization problem for continuous-time multiagent systems with general linear dynamics. The objective is to cooperatively optimize a team performance function formed by a sum of convex local objective functions. Each agent utilizes only local interaction and the gradient of its own local objective function. To achieve the cooperative goal, a couple of fully distributed optimal algorithms are designed. First, an edge-based adaptive algorithm is developed for linear multiagent systems with a class of convex local objective functions. Then, a node-based adaptive algorithm is constructed to solve the distributed optimization problem for a class of agents satisfying the bounded-input bounded-state stable property. Sufficient conditions are given to ensure that all agents reach a consensus while minimizing the team performance function. Finally, numerical examples are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Real number modeling of analog circuits in hardware description languages (HDLs) has become more common as a part of mixed-signal SoC validation. We propose two methods that both improve the fidelity and simulation speed, and make the event-driven, piecewise linear (PWL) analog functional models easier to write. First we use the accuracy set by users to dynamically determine when a new output segment should be emitted, which is computed without any iteration. This capability allows designers to trade accuracy for simulation speed of analog models without any time-consuming model calibration/error estimation, and creates models which generate events only when needed to maintain output accuracy. We next extend this method to eliminate limit-cycle oscillations that occur when simulating circuits with continuous-time feedback in a discrete-time event simulator. Handling this feedback efficiently allows the user to create the system model from simpler component models. The performance of this modeling approach is demonstrated on various analog filter models, an operational amplifier, and a high-speed, wireline transceiver system, and is 3.1 $\times$ faster than an optimally-chosen, fixed-time step simulation for the transceiver. [ABSTRACT FROM PUBLISHER]

We consider functions in the time and the frequency domain, and show how the occurrence of real zeros in the frequency domain is related to the number of zero crossings, overshoot and initial undershoot in the time domain. This leads to simple proofs of known facts for linear time-invariant systems and their generalizations in various directions. In particular, we consider time-delay systems and differential systems of fractional order. [ABSTRACT FROM AUTHOR]

Abstract: The stability of two-dimensional (2-D) linear discrete systems based on the Fornasini–Marchesini local state-space (LSS) model is considered. A stability criterion using the asymmetric Lyapunov matrix P is presented. A special case of the criterion is discussed. [Copyright &y& Elsevier]

A new linear method for solving the output feedback pole assignment problem of linear systems is introduced, and new sufficient conditions are obtained. [ABSTRACT FROM AUTHOR]

State estimation of stochastic discrete-time linear systems subject to persistent unknown inputs has been widely studied but only few works have been dedicated to the case where unknown inputs may be simultaneously or sequentially active or inactive. In this technical note, a Kalman filter approach is proposed for state estimation of systems with unknown intermittent inputs. The design is based on the minimisation of the trace of the state estimation error covariance matrix under the constraint that the state estimation error is decoupled from the unknown inputs corrupting the system at the current time. The necessary and sufficient stability conditions are established considering the upper bound of the prediction error covariance matrix. [ABSTRACT FROM PUBLISHER]

This technical brief proposes a new approach to stability analysis of linear systems with sampled-data inputs or channels. The method, based on a variation of the discrete-time Lyapunov approach, provides stability conditions using functional variables subject to convex constraints. These stability conditions can be solved using the sum of squares methodology with little or no conservatism in both the case of synchronous and asynchronous sampling. Numerical examples are included to show convergence. [ABSTRACT FROM AUTHOR]

Dissipativity is an important property of individual systems that guarantees a stable interconnected system. However, due to errors in the modeling process weakly non-dissipative models may be constructed. This paper introduces an enhanced method to perturb a non-dissipative LTI system in order to enforce dissipativity using spectral perturbation results for para-Hermitian pencils. Compared to earlier algorithms the new method is applicable to a wider class of problems, it utilizes a simpler framework, and employs a larger class of allowable perturbations resulting in smaller perturbations. Moreover, system stability can be enforced as well. Numerical examples are provided to show the effectiveness of the new approach. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we consider the simpler GMRES method augmented by approximate eigenvectors for solving nonsymmetric linear systems. We modify the augmented restarted simpler GMRES proposed by Boojhawon and Bhuruth to obtain a simpler GMRES with deflated restarting. Moreover, we also propose a residual-based simpler GMRES with deflated restarting, which is numerically more stable. The main advantage over the augmented version is that the simpler GMRES with deflated restarting requires less matrix-vector products per restart cycle. Some details of implementation are also considered. Numerical experiments show that the residual-based simpler GMRES with deflated restarting is effective. [Copyright &y& Elsevier]

We consider the problem of optimal decentralized controller synthesis. There are several classes of such problems for which effective solution methods are known, including the quadratically invariant one. In this technical note, we use Gröbner bases and elimination theory to characterize all closed-loop maps achievable by forming a feedback loop with decentralized controllers. We show that this approach allows solution of a wide class of optimal decentralized control problems; it includes not only quadratically invariant problems under a technical condition but also some other problems which are not quadratically invariant. [ABSTRACT FROM PUBLISHER]

Signal processing by means of analog circuits offers advantages from a power consumption viewpoint. A method is described to implement wavelets in analog circuits by fitting the impulse response of a linear system to the time-reversed wavelet function. The fitting is performed using local search involving an L2 criterion, starting from a deterministic starting point. This approach offers a large performance increase over previous Padé-based approaches and allows for the circuit implementation of a larger range of wavelet functions. Subsequently, using state-space optimization the dynamic range of the circuit is optimized. Finally, to illustrate the design procedure, a sixth-order L2-approximated orthonormal Gaussian wavelet filter using Gm-C integrators is presented. [ABSTRACT FROM PUBLISHER]

We develop a receding horizon control approach to stochastic linear systems with control and state multiplicative noise that also contain constraints. Our receding horizon formulation is based upon an on-line optimization that utilizes open-loop plus linear feedback and is solved as a semi-definite programming problem. We also provide a characterization of stability, performance, and constraint satisfaction properties of the receding horizon controlled system under a specific choice of terminal weight and terminal constraint. A simple numerical example is used to illustrate the approach. [ABSTRACT FROM AUTHOR]

This note continues on the results proposed in two previous papers for computing vector 1- or „-norm based Lyapunov functions for linear discrete-time systems by presenting a finitely terminating algorithm for the construction of Lyapunov functions of that class. The algorithm utilizes the solution of a finite sequence of feasibility linear programs (LPs) with very few constraints or, equivalently, very simple algebraic tests in contrast to solving the original problem where a bilinear matrix equation with rank and norm constraint needs to be solved. [ABSTRACT FROM AUTHOR]

We construct a continuous feedback for a saturated system x(t) = Axt(t) + Bσ(u(t)). The feedback renders the system asympototically stable on the whole set of states that can be driven to 0 with an open-loop control. The trajectories of the resulting closed-loop system are optimal for an auxiliary optimal control problem with a convex cost and linear dynamics. The value function for the auxiliary problem, which we show to be differentiable, serves as a Lyapunov function for the saturated system. Relating the saturated system, which is nonlinear, to an optimal control problem with linear dynamics is possible thanks to the monotone structure of saturation. [ABSTRACT FROM AUTHOR]

A computational test for scalar positive real and strictly positive real functions is proposed in this note. The input for this algorithm is state space representation, not necessarily minimal. It is derived for the discrete time problem, based on numerical stable eigenvalue computations. The test can be used in the continuous counterpart, which is in fact an improvement of an algorithm posed by Bai and Freund. Differences between the discrete and continuous time problems are also pointed out. [ABSTRACT FROM AUTHOR]

Models comprising, in sequence, linear analysers, Ψ1, …, Ψn, non-linear transducer functions, and the Minkowski decision rule, are widely used to fit detection and discrimination data, especially when necessary to take into account the effect of probability summation. However, the analysers’ characteristics cannot be derived from detection/discrimination data because of an unavoidable trade-off between these characteristics and the decision rule. Here we show how to overcome this problem, i.e. how to identify the analysers Ψi=∑, upper limit m aijφj=1 despite the probability summation between them. The observer''s performance is assumed to be quantitatively defined in terms of an equi-detection (discrimination) surface. Each analyser Ψi is expressed as a weighted sum of linear (coordinate) functionals φj:Ψ1,…,Ψn, so that an identification of the analysers ϕi is then reduced to evaluating the weight matrix A={aij}. It is proved that A can be uniquely recovered from a quadratic approximation of the equi-detection (discrimination) surface at the neighbourhood of at least two points. More specifically, the following equation holds true: ATD(AT)#=H1H2#, where A# is the generalised inverse of the matrix A, D is an unknown diagonal matrix, H1 and H2 are the matrices of the quadratic forms determining the quadratic surfaces approximating the equi-detection (discrimination) surface at two different points. Thus, the matrix H1H2# known from experiment is a similarity transform of the diagonal matrix, the rows of A being the eigenvectors of H1H2#. Hence, any eigensystem routine can be used to derive A from H1H2#. [Copyright &y& Elsevier]

This paper focuses on the problem of H∞-control design for linear systems with multiple time-delays, in which the controlled output contains delayed states and disturbance input. The proposed H∞-control problem for a class of linear systems with time-delays is realized as an H∞-control problem for an auxiliary linear system free of time-delay. A new explicit design for dynamic output feedback H∞ controllers is obtained. In addition, a numerical example is presented to illustrate the effectiveness of the proposed approach. [Copyright &y& Elsevier]