LPV system analysis via quadratic separator for uncertain implicit systems

This paper considers a class of linear systems containing time-varying parameters whose behavior is not known exactly. We assume that the parameters vary within known intervals and there are known bounds on their rates of variation. We give a computationally verifiable condition for stability of the system for all possible parameter variations. In particular, we first show that the information on the rate bounds can be exploited by considering an augmented system described by an implicit model. Through the analysis of the implicit system using the quadratic separator, we obtain a sufficient stability condition for the original system. Moreover, we show that the condition thus obtained is equivalent to the existence of a Lyapunov function that depends on the parameters in a linear fractional manner. Finally, the computational aspects of the proposed stability conditions are addressed in terms of linear matrix inequalities which can be solved efficiently via interior point methods