Sliding Mode Control for Markov Jump Systems With Delays via Asynchronous Approach
针对一类含不确定性和时滞的非线性连续时间马尔可夫跳变系统，设计了一种异步滑模控制器，保证系统轨迹在有限时间内到达切换滑模面，并分析了随机稳定性与耗散性能。
In this paper, the problem of sliding mode control (SMC) is considered for a class of nonlinear continuous-time Markov jump systems (MJSs) with uncertainties and time delay. A novel integral-type switching sliding surface function is designed, where the controller gain may jump asynchronously with original MJSs. Then, an SMC law is constructed to force system trajectories onto the specified switching sliding surface in a finite time. The stochastic stability and dissipative performance of sliding mode dynamics are analyzed and the delay-dependent sufficient condition for the existence of the desired switching surface is developed. Moreover, we also extend SMC to investigate the finite-time stability problem during both reaching phase and sliding motion phase in the stochastic setting. Finally, simulation results are given to illustrate the effectiveness of the proposed design techniques.