Composite Anti-disturbance Control of Markovian Jump Systems

Abstract

This chapter considers anti-disturbance control problem for Markovian jump systems. We propose a composite hierarchical anti-disturbance (CHAD) control methodology, that is, disturbance-observer-based (DOB) control plus $\mathcal {H}_{\infty }$ control, for the considered systems with nonlinearity and multiple disturbances. The nonlinearity with known and unknown functions is considered, respectively. The multiple disturbances include two kinds: one is supposed to be a norm-bounded vector; the other is described by an exogenous system with perturbations. With the introduction of notion of composite DOB control and $\mathcal {H}_{\infty }$ control and by choosing a proper stochastic Lyapunov–Krasovskii functional, disturbance observers and special controllers are solved, such that the composite system is stochastically stable, and meets certain performance requirements.