Robust Stability/Performance Analysis for Linear Time-Invariant Polytopically 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 polytopically parameter-dependent, and PDLFs are set to be polynomially parameter-dependent with respect to parameters which represent vertices of the polytope. 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. To compare our methods with existing methods, we introduce many examples borrowed from existing papers and demonstrate the effectiveness of our results compared with them.