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This study addresses the stability problem for linear continuous‐time Markovian switching singular systems. Based on a refined description for jumps of the system states at the switching instants, sufficient conditions for exponential stability in the mean‐square sense of the Markovian switching singular system are obtained by means of multiple Lyapunov function method. The obtained results present a new analysis of the impact for switching law‐induced state jump on the stability property of the considered system. Numerical examples are presented to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses the state estimation and stabilization for linear discrete-time descriptor systems. It is assumed that the estimator and controller can only receive the transmitted sequence of finite coded signals via a limited digital communication channel. Both coder–decoder and coder–decoder–controller procedures are proposed, in which a compensation term is introduced to meet the compatible requirement. In addition, an effective method for selecting the compensation term is presented. Detection and stabilization conditions in terms of linear matrix inequality are obtained. Finally, an example is given to illustrate the effectiveness of design procedures. [Copyright &y& Elsevier]

This paper considers the event-triggered H ∞ filtering problem for continuous-time switched linear systems. It is assumed that only the information of system output and switching signal is available to the filter at each event-triggered sampling instant. Based on a mode dependent event-triggered sampling scheme, the filtering error system is modeled as a switched system with augmented switching signal. Then, by the average dwell time technique and multiple Lyapunov function method, a new sufficient condition is obtained such that the filtering error system is exponentially asymptotically stable and satisfies the weighted H ∞ performance. The design method for the filter and event-triggered parameters is formulated by solving a set of linear matrix inequalities. Finally, the effectiveness of the proposed approach is illustrated by two numerical examples. [ABSTRACT FROM AUTHOR]

Abstract: The simultaneous semi-global -stabilization and asymptotic stabilization in both semi-global and global cases are considered for continuous-time linear singular systems subject to input saturation. Based on the asymptotical property of the parametric generalized algebraic Riccati equations, a low-and-high gain state feedback control law and a scheduling technique are proposed. When applied to the singular system subject to input saturation and external disturbance, the semi-global finite-gain -stabilization and semi-global/global asymptotic stabilization are obtained simultaneously. The obtained results reduce to the existing ones for non-singular linear systems when the linear singular system reduces to a non-singular system. Furthermore, our results also improve the semi-global stabilization results for singular systems with saturation in the absence of the external disturbance. [Copyright &y& Elsevier]

The event-triggered control problem for discrete-time switched linear systems with network transmission delays is investigated in this paper. It is assumed that the controller can only access the transmitted information of system state and mode at each event-triggered instant. A mode dependent event-triggered transmission scheme is proposed and the closed-loop system is modeled as a switched system with delayed state and augmented switching signal. Then based on the multiple Lyapunov functional method, an exponential stability condition and design method for state feedback controller gains are obtained. The proposed approach leads an important step to study the event-triggered control for discrete-time switched systems. Finally, the effectiveness and improvement of the proposed approach are illustrated by a numerical example. [ABSTRACT FROM AUTHOR]