Special time-varying Lyapunov function for robust stability analysis of linear parameter varying systems with bounded parameter variation

Abstract

The robust stability of linear continuous-time uncertain systems in polytopic domains is investigated. The uncertain parameters are assumed as time varying with bounded rates of variation. The robust stability conditions are obtained from the definition of a Lyapunov function with a particular structure, depending on integer powers κ of the dynamic uncertain time-varying matrix of the system and on a parameter-dependent matrix to be determined. As a consequence, parametrised linear matrix inequality conditions can be derived in terms of κ for a particular structure of the decision variables. As κ grows, the robust stability conditions can take into account bounds on the successive time derivatives of the uncertain parameters whenever this information is available, reducing the conservativeness of the evaluations. Numerical examples illustrate the effectiveness of the proposed methodology.