A Linear Matrix Inequality Approach

This paper addresses the problem of designing stabilizing controllers that minimize the 7 l ~ norm of a certain closed-loop transfer function while maintaining the C1 norm of a different transfer function below a prespecified level. This problem arises in the context of rejecting both stochastic as well as bounded persistent disturbances. Alternatively, in a robust control framework it can be thought as the problem of designing a controller that achieves good nominal 7-12 performance, while a t the same time, guaranteeing stability against unmodeled dynamics with bounded induced C, norm. The main result of this paper shows that, for the state feedback case, a suboptimal static feedback controller can be synthesized by a two stage process involving a finitedimensional convex optimization problem and a line-search.