Variance-constrained control for uncertain stochastic systems via disturbance observers

In this paper, the robust variance-constrained composite control problem is investigated for linear uncertain discrete-time stochastic systems. The parameter uncertainties are allowed to be norm-bounded and enter into the state matrix. The purpose of this problem is to design a disturbance observer to estimate the disturbance generated by an exogenous system, then construct the control strategy by integrating the output of the disturbance observer with state-feedback control law, such that, for all admissible parameter uncertainties, the system state of the closed-loop system is mean square bounded, and the steady state variance of each state is not more than the individual prescribed upper bound. And a LMI method is developed to deal with the control problem, which is related to a linear matrix inequality. An illustrative numerical example is provided to demonstrate the effectiveness of the proposed design approach.