State-feedback H∞ Control for Nonlinear Stochastic Systems with Markovian Jumps in Infinite Time Horizon

Abstract

This paper discusses the H∞ control problem for a class of nonlinear stochastic systems with Markovian jumps subjected to both state- and disturbance-dependent noise. We establish the equivalent conditions among Hamilton-Jacobi inequality (HJI), Hamilton-Jacobi equality (HJE), the dissipative inequality and L2-gain property for this class of systems. As to the infinite time horizon case, we synthesize a worst case-based state-feedback H∞ controller.