Output feedback controllers for systems with structured uncertainty

This paper deals with design of compensators that provide a guaranteed level of performance, in the sense of L₂ gain, for systems with time-varying structured uncertainty. For stability, the notion of quadratic stability, using a single Lyapunov function, is used. The uncertainty is assumed to be polytopic (e.g. the uncertainty vector enters the state space representation of the systems affinely). Previous results in the characterization of H_∞ controllers are used to show that quadratic stability with performance is equivalent to a bi-affine problem. A set of conditions, under which the problem becomes convex, are discussed