Parameter-dependent Lyapunov functions, constant real parameter uncertainty, and the Popov criterion in robust analysis and synthesis. I

Abstract

A framework for parameter-dependent Lyapunov functions, a less conservative refinement of 'fixed' Lyapunov functions, is developed. An immediate application of this framework is a reinterpretation of the classical Popov criterion as a parameter-dependent Lyapunov function. This observation is exploited to obtain conditions for robust controller synthesis with full-state, full-order, and reduced-order controllers in H/sub 2/ and H/sub 2//H/sub infinity / settings.