Model reference tracking control for discrete stochastic bilinear systems with time-varying delays

This paper is concerned with the problem of model reference tracking control for a class of discrete-time stochastic bilinear systems with interval time-varying delays. The purpose is to design a state-feedback controller such that the state of the controlled system tracks a reference signal generated by a stable linear model. First, a new stability criterion for the considered systems is obtained. It is shown through a numerical example that the obtained stability criterion is less conservative than the recent ones in the literature. Second, delay-dependent conditions for the solvability of the addressed tracking problem are obtained in terms of linear matrix inequalities (LMIs). The desired controller gains can be constructed by using feasible solutions to the presented LMIs. Finally, a numerical example including simulations is provided to illustrate the effectiveness of the proposed design method.