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 H_∞ control of linear systems with real convex polytopic uncertainties. In order to use a parameter-dependent Lyapunov function for a system with polytopic uncertainties, the derivative term for the state, which is in the derivative of the Lyapunov function, is reserved; and free weighting matrices are used to express the relationship between the terms of the system equation. This yields a new linear-matrix-inequality approach to BRL representation. In addition, this method is extended to the design of a state-feedback controller that solves the H_∞ control problem. Numerical examples demonstrate that the proposed method is effective and is an improvement over previous ones.