Sliding mode control of discrete‐time switched systems subject to mode delays

Abstract

Summary This work considers the sliding mode control problem of a class of discrete‐time uncertain switched systems subject to detecting‐delay on mode signals, which may result in the asynchronous phenomenon between the controller and the switched system. Since the mode information of the controlled system is not available for the controller in time, a mode‐independent sliding surface will be introduced, by which an asynchronous sliding mode controller is designed, whose control gain and robust parameter will be changing according to the controller mode. In the analysis on the stability of the closed‐loop control system and the reachability of the specified sliding surface, the asynchronous characteristics are detailedly investigated. It is shown that the Lyapunov function may be not always decreasing along the state trajectories during the unmatched interval of controller modes and system modes. Nevertheless, it is proven that the state trajectories can be driven into a sliding region around the specified sliding surface in finite time. Finally, some numerical simulation results are provided.

Finite‐time boundedness of sliding mode control under periodic event‐triggered strategy

“…the state trajectories of the closed-loop system (10) can arrive at the sliding surface s(t) = 0 at the instant T * with T * < T, and remain within the following domain  around the specified surface for t ∈ [T * , T]:…”

“…The basic idea of SMC is to force the system trajectories of the controlled system onto a pre-designed sliding surface, and maintain them there for all subsequent time. [9][10][11][12][13] Moreover, a partitioning strategy was put forward in Reference 5 to analyze the FTB cover the reaching and the sliding phases, respectively. This interesting results have been also extended to various complex systems including switched systems, 6 fuzzy systems, 7 and Markov jump systems.…”

“…Recently, some interesting works concerning the sliding mode control (SMC) problem satisfying the requirement of FTB have been presented in References 5‐8. The basic idea of SMC is to force the system trajectories of the controlled system onto a pre‐designed sliding surface, and maintain them there for all subsequent time 9‐13 . Moreover, a partitioning strategy was put forward in Reference 5 to analyze the FTB cover the reaching and the sliding phases, respectively.…”

Dynamic output feedback sliding mode control for Markovian jump systems under stochastic communication protocol and its application

“…Sliding mode control (SMC) has long been a question of great interest in a wide range of fields since the sliding mode dynamics have the insensitivity to matched uncertainties and external perturbations on the sliding surface. [17][18][19][20][21] The communication protocol problems have been considered using the SMC method in References 13,15, where a sliding mode controller has been constructed in Reference 15 to achieve a prescribed H ∞ performance level subject to the SCP scheduling. More recently, the SMC has been extended to the Markovian jump systems (MJSs) to deal with the network induced phenomena, [22][23][24][25][26][27] because MJSs can effectively characterize abrupt variations in system structures and model some complicated NCSs.…”

“…Sliding mode control (SMC) has long been a question of great interest in a wide range of fields since the sliding mode dynamics have the insensitivity to matched uncertainties and external perturbations on the sliding surface 17‐21 . The communication protocol problems have been considered using the SMC method in References 13,15, where a sliding mode controller has been constructed in Reference 15 to achieve a prescribed H ∞ performance level subject to the SCP scheduling.…”