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A new type of asymptotic stability for nonlinear hybrid neutral stochastic systems with constant delays was investigated recently, where the criteria depended on the delays’ sizes. Unfortunately, developed theory so far is not sufficient to deal with challenging problems of the decay rate, time-varying delays, and nonautonomous issues. These problems have not been tackled in the existing literature. Consequently, under the weak constraints, this article focuses on the general decay, including the exponential stability and the polynomial stability, for nonlinear nonautonomous hybrid neutral stochastic systems with time-varying delays by the approach of the multiple degenerate functionals. Moreover, this article derives the interesting assertions related to the general $H_{\infty }$ stability and the polynomial growth at most. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of event-triggered H ∞ state estimation for switched genetic regulatory networks with static coupling via a sojourn-probability-dependent approach. The measurements of the network are evaluated by the event-triggers which are only undertaken at the switching times. By employing a time-delay approach, the estimation can be achieved by determining the exponential mean-square stability of the switched system with time-varying delay and known sojourn probability, while the system prescribes an H ∞ performance level. A co-design approach for the event-triggered mechanism and the estimators is presented by means of a novel Lyapunov–Krasovskii functional combining with refined Jensen-based inequalities. Finally, a numerical example is given to demonstrate the effectiveness of the designed estimators. [ABSTRACT FROM AUTHOR]

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]

SUMMARY This paper discusses the exponential stability and stabilization for nonlinear descriptor systems with discrete and distributed delays. In terms of the Lyapunov method, the exponential stability of the slow subsystem is firstly obtained. Then, a new homotopy-based approach is proposed to investigate the exponential stability of the fast subsystem. By an estimate of the weighted matrix norm for a nonlinear mapping, the exponential stability of the fast subsystem and thus delay-dependent sufficient conditions for the exponential stability of the systems are obtained. In addition, a state feedback controller is designed for the stabilization of the nonlinear descriptor systems. Finally, the effectiveness of the proposed approach is illustrated by numerical examples. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

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]