Robust stabilization of periodic and multirate systems with gap and ν-gap uncertainty

In this paper we present a state space solution to the robust stabilization problem of general discrete-time periodic and multirate systems where the uncertainty is described in terms of the gap and nu-gap metrics. This robust stability problem is converted to a constrained H-infinity 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. Copyright (C)2001 IFAC.