Robust performance for uncertain systems via Lyapunov functions with higher order terms

Abstract

It is proposed in this paper new linear matrix inequality (LMI) conditions to certify stability and robust performance in terms of the H∞ guaranteed cost for uncertain linear time-invariant continuous and discrete-time systems. The proposed conditions are based on the existence of a Lyapunov function that considers higher order state derivatives for continuous-time systems and higher order state shifts for discrete-time systems. Moreover, the Lyapunov candidate function depends on the uncertain system matrices and on the polynomial structure imposed to the candidate Lyapunov matrices. Benchmark examples from the literature illustrate the performance, in terms of scalar decision variables and LMI rows, of the proposed method when compared to other approaches.