Robust Stability/Performance Analysis for Linear Time-Invariant Polynomially Parameter-Dependent Systems Using Polynomially Parameter-Dependent Lyapunov Functions

Abstract

This paper addresses robust stability,_H2 performance, and H_∞ performance analysis for Linear Time-Invariant Parameter-Dependent (LTIPD) systems using Parameter-Dependent Lyapunov Functions (PDLFs). The statespace matrices of the LTIPD systems are set to be parameter-dependent in negative as well as positive power series with respect to the parameters, and PDLFs are also set to be parameter-dependent in negative as well as positive power series with respect to the parameters. Our results are derived using“slack variables” and restricting them to be parameter-independent, therefore, they are only sufficient conditions for the original analysis problems. However, we demonstrate the effectiveness of our results with randomly generated numerical examples and several numerical examples which are borrowed from existing papers.