Lifted versions of robust D-stability and D-stabilisation conditions for uncertain polytopic linear systems

Abstract

This study aims at developing new linear matrix inequality (LMI) conditions for robust κ-stability and κ-stabilisation of linear time-invariant uncertain systems in polytopic domains. An existing LMI condition for robust κ-stability is lifted into those of larger dimensions that are given as functions of a certain integer κ. Based on the consequent conditions, new sufficient conditions for the existence of a state-feedback control law ensuring the robust κ-stability of the closed-loop system is proposed in terms of LMIs. Finally, examples are given to illustrate the benefit of the proposed methods.