Analysis of robust stability of time-varying parameter polynomial-dependent linear systems

Based on the parameter-dependent Lyapunov function and S-procedure approach, this article presents a novel analysis approach to robust stability of single time-varying parameter, polynomial-dependent linear systems with polynomial degree L. The article gives not only a stability criterion obtained from the feasibility test in terms of a pair of linear matrix inequalities (LMIs) containing parameter and its changing- rate bounds, and coefficient matrices of the polynomial, but also an algorithm to find the maximal parameter bound under a stable nominal system and a given parameter changing-rate bound. Some well-known previous results are encompassed as our special cases. Numerical examples are included for illustrating efficiency of our approach.