Robust stability analysis of time-varying parameter polynomial-dependent linear systems

The article proposes a novel approach to robust stability analysis of linear parameter-varying systems, of which the system matrix is polynomial-dependent on a time-varying parameter with degree L. The robust asymptotically stability of the system is transformed into feasibility test of a pair of linear matrix inequalities (LMIs) that include the parameter, its varying-rate bound and given coefficient matrices. The result presented in this article is less conservative comparing with the previous results that are based on either quadratic Lyapunov function, or a parameter-dependent Lyapunov function, respectively. A numerical example shows the validity of the result.