Robust stability/performance analysis for uncertain linear systems via multiple Slack Variable Approach: Polynomial LTIPD systems

This paper addresses robust stability, H-2 performance, and H-infinity performance analysis for Linear Time-Invariant Parameter-Dependent (LTIPD) systems, in which the state-space matrices are polynomially parameter-dependent, using polynomially Parameter-Dependent Lyapunov Functions (PDLFs). Our results are derived via multiple "slack variable" approach, which has previously been proposed for the non-negativity check of polynomial functions and it has been proved that the conservatism is no more than SOS approach. Our derived conditions are only sufficient conditions for the original problems; however, they encompass the previously proposed methods using single slack variables. We illustrate the effectiveness of our methods with randomly generated numerical examples compared to the methods using single slack variables.