Finite‐time stabilization of Markovian jump delay systems – a switching control approach

Abstract

Summary In this paper, a finite‐time stabilization problem is considered for a class of continuous‐time Markovian jump delay systems (MJDSs). A switching controller, which only depends on the average dwell time (ADT) switching laws, is proposed to make a trade‐off between robustness and adaptiveness when the design complexity of mode‐independent, mode‐dependent, and mode‐dependent and variation‐dependent control strategies is considered. First, the stochastic finite‐time boundedness for an MJDS is analyzed by an ADT approach. Second, the disturbance attenuation capability of MJDS is studied via a finite‐time weighted L2 gain, which depends on the switching numbers. The impacts of finite‐time interval and L2 gain acting on the ADT are also thoroughly discussed. Then, a switching controller is designed such that the resulting closed‐loop MJDS is stochastically finite‐time bounded and has a guaranteed disturbance attenuation level. Finally, a numerical example is provided to verify the effectiveness of the developed results. Copyright © 2016 John Wiley & Sons, Ltd.

Feedback stabilization of multi‐DOF nonlinear stochastic Markovian jump systems

“…The early research concentrated mainly on the linear MJSs. During the recent years, a large number of research activities have been concerned on the nonlinear MJSs . For example, sliding mode control is extended to robust stabilization of nonlinear MJSs and the ergodic control problem of nonlinear MJSs is studied based on the dynamic programming principle .…”

“…During the recent years, a large number of research activities have been concerned on the nonlinear MJSs. [11][12][13][14][15][16][17][18] For example, sliding mode control is extended to robust stabilization of nonlinear MJSs 19,20 and the ergodic control problem of nonlinear MJSs is studied based on the dynamic programming principle. 21,22 However, most of the work done on stabilization and control is built upon the assumption of the MJSs without stochastically driven.…”

Observer‐based H∞ control for Markovian jump systems with time‐varying delays and incomplete transition rates

“…As we know, time delays widely exist in various systems, which may degrade system performance or even make it unstable . With the rapid development of robust control techniques, many methods were proposed to deal with delay‐dependent criteria for the time‐delay systems.…”

“…As we know, time delays widely exist in various systems, 2,25-27 which may degrade system performance or even make it unstable. [28][29][30][31][32] With the rapid development of robust control techniques, many methods were proposed to deal with delay-dependent criteria for the time-delay systems. Particularly, a method of reducing the conservatism effectively (called delay partitioning method) was first proposed.…”

Finite-time event-triggered control and fault detection for singular Markovian jump mixed delay systems under asynchronous switching

“…Now, many interesting results have been obtained for this type of stability. For example, [24] investigated the problem of robust finite-time boundedness of H ∞ filtering for switch systems with time-varying delay; [25] addressed a finite-time stabilization problem for a class of continuous-time Markovian jump delay systems with switching control approach; [26] studied observerbased state feedback finite-time control for nonlinear jump systems with time-delay and [27] dealt with the finite-time synchronization problem for a class of uncertain coupled switched neural networks under asynchronous switching.…”