Time-delay is unavoidable, encountered in many practical systems such as networked control systems, communication networks, manufacturing, and biology. On the one hand, it often represents a source ...of instability and oscillation. On the other hand, the appearance of delay can have a stabilizing effect, and delayed feedback control can be used to stabilize some unstable systems. Considering its theoretical and practical importance, increasing attention has been focused on the analysis and synthesis of time-delay systems, and various new approaches have been proposed to reduce their conservatism. The aim of reducing the conservatism of delay-dependent stability criteria is to establish new stability criteria to provide a maximal allowable delay as large as possible. Among different techniques, the reduced conservatism is mainly obtained by constructing an improved Lyapunov functional and employing a tighter bound on some weighted cross products. A great number of effective methods have been provided such as delay-partitioning method, convex combination method, Wirtinger-based inequality, and Bessel-Legendre inequality.
We study an interconnection between a switched affine system and a fast LTI dynamics. Often, the classical stabilization method based on the existence of a stable convex combination is directly used ...for systems on two time scales while using only the slow dynamics. Here, we provide conditions for checking the Uniform Ultimate Boundedness when the fast dynamics is taken into account. In addition, criteria for verifying asymptotical stability are provided for a special case. Numerical examples illustrate the main results.
This paper deals with the switching law design problem for discrete-time switched affine systems. While the existing literature addresses the case of globally stabilizing switching laws, in discrete ...time, many switched affine systems can only be stabilized locally. In this work, methods are proposed for the design of switching control laws ensuring the local uniform ultimate boundedness of the equilibrium. The approach is based on the existence of a stabilizing continuous state feedback for a bilinear system. Estimates of the domain of attraction and of the invariant attractive neighborhood of the equilibrium are given. Numerical methods that allow a simple implementation of the proposed results are given.
This article presents basic concepts and recent research directions about the stability of sampled-data systems with aperiodic sampling. We focus mainly on the stability problem for systems with ...arbitrary time-varying sampling intervals which has been addressed in several areas of research in Control Theory. Systems with aperiodic sampling can be seen as time-delay systems, hybrid systems, Input/Output interconnections, discrete-time systems with time-varying parameters, etc. The goal of the article is to provide a structural overview of the progress made on the stability analysis problem. Without being exhaustive, which would be neither possible nor useful, we try to bring together results from diverse communities and present them in a unified manner. For each of the existing approaches, the basic concepts, fundamental results, converse stability theorems (when available), and relations with the other approaches are discussed in detail. Results concerning extensions of Lyapunov and frequency domain methods for systems with aperiodic sampling are recalled, as they allow to derive constructive stability conditions. Furthermore, numerical criteria are presented while indicating the sources of conservatism, the problems that remain open and the possible directions of improvement. At last, some emerging research directions, such as the design of stabilizing sampling sequences, are briefly discussed.
This paper addresses the stability analysis problem for a class of linear hyperbolic systems with distributed controllers sampled in space and time. First, the considered system is recast in an ...equivalent form with a continuous time control loop and operators representing the discretization errors (spatio-temporal sampling errors). Then with the help of the Lyapunov–Razumikhin approach, the Rɛ-stability of the proposed linear hyperbolic systems of balance laws is verified via sufficient conditions. At last, the proposed method is illustrated numerically.
This paper deals with the exponential stability analysis of decentralized, sampled-data, Linear Time Invariant (LTI) control systems with asynchronous sensors and actuators. We consider the case ...where each controller in the decentralized setting has its own sampling and actuation frequency, which translates to asynchrony between sensors and actuators. Additionally, asynchrony may be induced by delays between the sampling instants and actuation update instants as relevant in a networked context. The decentralized, asynchronous LTI system is represented as the feedback interconnection of a continuous-time LTI system operator and an operator that captures the effects of asynchrony induced by sampling and delay. By characterizing the properties of the operators using small-gain type Integral Quadratic Constraints (IQC), we provide criteria for exponential stability of the asynchronous, decentralized LTI state-space models. The approach provided in this paper considers two scenarios, namely the ‘large-delay’ case and the ‘small-delay’ case where the delays are larger and smaller than the sampling interval, respectively. The effectiveness of the proposed results is corroborated by a numerical example.
In this paper, we provide novel conditions for stability analysis of aperiodically sampled nonlinear control systems subjected to time-varying delay. The proposed approach can also deal with cases in ...which delay is larger than the sampling interval. It is applicable to a general class of nonlinear systems and provides sufficient criteria for stability that aid in making trade-offs between control performance and the bounds on sampling interval and delay. As a stepping stone, a preliminary and generic result based on dissipativity, is introduced to analyse the exponential stability of a class of feedback-interconnected systems. The nonlinear sampled-data system is remodelled to consider the effects of sampling and delay in the dissipativity framework, as perturbations to the nominal closed-loop system. This leads to constructive stability conditions for a continuous time closed-loop system given by the feedback interconnection of the nominal closed-loop system and an operator(s) that captures the effects of sampling and delay. For Linear Time-Invariant (LTI) systems, we recover simple Linear Matrix Inequality (LMI) and frequency domain conditions previously proposed in the robust control framework.
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