H∞ control with state constraints

In this paper we present a biconvex programming approach for the design of output feedback controllers for discrete-time systems. The method is based on necessary and sufficient conditions for the existence of stabilizing static output feedback controllers. An interesting feature of the solution is that the matrix of output feedback gains is given explicitly. Then, we show how convex design constraints can be incorporated in the proposed design approach. Mixed frequency and time domain specifications for the closed-loop system like H_∞ performance requirements and state constraints in the presence of disturbances are considered