Parameter-dependent Lyapunov functions for robust stability analysis of time-varying systems in polytopic domains

The robust stability of linear continuous-time uncertain systems in polytopic domains is investigated in this paper. 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 kappa of the dynamic uncertain matrix of the system. As a consequence, parametrized linear matrix inequalities conditions are obtained in terms of kappa. As kappa grows, the robust stability conditions can take into account bounds on the successive time-derivatives of the uncertain parameters, reducing the conservativeness of the evaluations. Numerical examples illustrate the effectiveness of the proposed methodology.