A state space solution to the robust stabilization problem of discrete-time multirate and periodic systems

In this paper we present a state space solution to the robust stabilization problem of general discrete-time multirate and periodic systems where the uncertainty is described in terms of the gap and ν-gap metric. This robust stability problem is converted to a constrained H_∞ optimal control problem by using the lifting technique. Then the optimal robust stability margin is explicitly computed and a method is provided to get the controllers satisfying the optimal robust stabilization margin. The solution amounts to solving two discrete-time algebraic Riccati equations and an extended Parrot problem.