Fixed-time sliding mode controller design for a class of nonlinear Markovian jumping systems

摘要

In this paper, a sliding mode control (SMC) strategy is applied to investigate the fixed-time stabilization (FTS) problems for nonlinear Markovian jumping systems (NMJSs) with nonlinear parts satisfying conic conditions. We aim to design a suitable SMC law to drive the system state trajectories onto the specified sliding mode surfaces (SMS) within a specified fixed-time interval. Then, by using the slack matrix approach, the sufficient conditions are derived to ensure the FTS of MJSs during the reaching phase. An appropriate Lyapunov-Krasovskii functional method is given to guarantee the FTS of the NMJSs during the slidinging motion phase. Finally, the FTS condition of the NMJSs in the whole fixed-time interval is given and proved. The effectiveness of the method is verified by a simulation result related to the Chua's circuit. (C) 2020 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.