Dissipativity-Based Sliding Mode Control of Switched Stochastic Systems

• Published in: IEEE transactions on automatic control Vol. 58; no. 3; pp. 785 - 791
• Main Authors: Wu, Ligang, Zheng, Wei Xing, Gao, Huijun
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2013; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Average dwell time; Dissipation; dissipativity; Dynamic tests; Dynamical systems; Dynamics; mean-square exponential stability; Sliding; Sliding mode; Sliding mode control; Stability analysis; Stochastic systems; Switched systems; Switches; Symmetric matrices; Trajectory
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2012.2211456

This technical brief is concerned with dissipativity analysis and dissipativity-based sliding mode control (SMC) of continuous-time switched stochastic systems. Firstly, a sufficient condition is proposed to guarantee the mean-square exponential stability and strict dissipativity for the switched stochastic system. Then, an integral-type sliding surface function is designed for establishing a sliding mode dynamics, which can be formulated by a switched stochastic system with an external disturbance/uncertainty. Dissipativity analysis and synthesis are both investigated for the sliding mode dynamics, and consequently sufficient conditions are derived, which pave the way for solving the dissipativity analysis and control problems. Moreover, a SMC law is synthesized to drive the system trajectories onto the predefined sliding surface in a finite time. Finally, the efficiency of the theoretical findings is demonstrated by an illustrative example.