Sliding Mode Control of Uncertain Parameter-Switching Hybrid Systems

12SMC with Dissipativity of Switched Stochastic Hybrid Systems

12.1 Introduction

Dissipativity theory has played a critical part in analysis and control design of linear and nonlinear systems, especially for high-order systems, since from the practical application point of view, many systems need to be dissipative for achieving effective noise attenuation. It has been recognized that for more abstract systems one can still associate with them an energy-like function (called the storage function) and an input-power-like function (called the supply rate). Dissipativity is then characterized by storage functions and supply rates, which represent the energy stored inside the system and energy supplied from outside the system, respectively. Roughly speaking, dissipative systems are those for which the increase in stored energy is never larger than the amount of energy supplied by the environment, that is, dissipative systems can only dissipate but also not generate energy. The dissipative systems theory is closely related to the dynamic properties of a process and, in particular, to its stability properties.

In this chapter, we will study dissipativity analysis and SMC design for switched stochastic hybrid systems. A more general supply rate is proposed, and a strict -dissipativity is defined, which includes , positive realness, and passivity as its special cases. The main idea is ...