Improved bounded-real-lemma representation and H∞ control of systems with polytopic uncertainties

This brief concerns the problem of the bounded-real- lemma (BRL) representation and control of linear systems with real convex polytopic uncertainties. In order to use a param- eter-dependent Lyapunov function for a system with polytopic un- certainties, the derivative term for the state, which is in the deriva- tive of the Lyapunov function, is reserved; and free weighting ma- trices are used to express the relationship between the terms of the system equation. This yields a new linear-matrix-inequality ap- proach to BRL representation. In addition, this method is extended to the design of a state-feedback controller that solves the con- trol problem. Numerical examples demonstrate that the proposed method is effective and is an improvement over previous ones. Index Terms—Bounded-real-lemma (BRL), control, linear matrix inequality (LMI), parameter-dependent Lyapunov func- tion, polytopic uncertainty.