Switched state-feedback control of discrete-time linear systems with multiplicative noises

In this paper we consider the switched stochastic control problem of discrete-time linear systems with multiplicative noises. The control strategy is composed by a state-feedback switched component combined with a linear state-feedback part. We present a sufficient condition to derive the state feedback gains and the switching rule jointly so that the closed loop system is stochastic stable and a performance cost is bounded above by a constant value. The case without the linear state-feedback part is also considered. This sufficient condition is based on the so-called Lyapunov-Metzler inequalities. The results are illustrated with a portfolio tracking control problem.