State-feedback $H_\infty$ stabilization of state-dependent jump linear systems

Abstract

International audienceA state-dependent jump linear system (SDJLS) is a particular type of stochastic switching system, where the transition rates or probabilities of the underlying random jump process depend on the state variable. In this paper, a continuous-time SDJLS subject to external disturbances with finite energy is considered. Regarding the underlying random jump process, the transition rates are assumed to have different values across different sets where the state of the system evolves. By evaluating the infinitesimal generator for the stochastic Lyapunov function of SDJLS, a state-feedback H infinity controller is synthesized that guarantees disturbance rejection while ensuring stochastic stability via solving a set of sufficient linear matrix inequalities. The overall approach is illustrated with a numerical example