Stochastic control of state‐dependent jump linear systems with state‐dependent noise

Abstract

State-dependent jump linear systems (SJLSs) are a set of linear systems whose switching is determined by a finite state random process with state-dependent transition rates. In this study, a SJLS is considered with state multiplicative noise and stochastic perturbations. In particular, the jump process is regarded to have dissimilar transition rates among sets of state evolution space. The aim of this study is to consider stochastic H ∞ control of such systems using state-feedback control input. Sufficient conditions for stochastic H ∞ are obtained by solving linear matrix inequalities, which are validated by a simulation example.