Event-triggering dissipative control of switched stochastic systems via sliding mode

Abstract

This paper is concerned with the mean-square exponential stability and performance analysis, stabilization, dissipative control and dissipativity-based sliding mode control (SMC) problems for discrete-time switched stochastic hybrid systems. Such systems can be also regarded as switched hybrid systems with stochastic perturbation. Event detectors, which can save computational resource, are designed to determine whether the current data should be transmitted or not in the design process. Firstly, by proposing an average dwell time method combining with a switched (mode-dependent) Lyapunov function, a sufficient condition is established under the event-triggering scheme, which guarantees that the considered switched stochastic system is mean-square exponentially stable, and then an explicit parametrization of the desired stabilization controller is also given. Secondly, the event-triggering dissipativity analysis and the dissipative control problems are investigated. A dissipativity performance condition is proposed to guarantee the mean-square exponential stability and strict dissipativity for the discrete-time switched stochastic system, and then the dissipative controller is implemented by the state feedback. Thirdly, a switched observer is constructed to estimate unavailable state variables, based on which a differential-type sliding surface function is designed, with which the sliding mode dynamical equations can be easily obtained. The resulting closed-loop system with sliding mode dynamics is an autonomous switched stochastic system. Dissipativity analysis and synthesis are both investigated for the closed-loop system, and consequently sufficient conditions are derived, which pave the way for solving the event-triggering observer-based dissipative sliding mode control problem. Moreover, an event-triggering output-based SMC law is first synthesized to drive the system trajectories to enter a predefined sliding vicinity. Finally, illustrative examples are employed to validate the proposed controller design schemes.