Parameter-dependent Lyapunov function approach to robust stability analysis for discrete-time descriptor polytopic systems

This paper investigates robust stability of discrete-time descriptor polytopic systems (DTDPSs for short). The concept of affine generalized quadratic stability, which has less conservatism than generalized quadratic stability, of DTDPSs is proposed. It not only investigates affine generalized quadratic stability of DTDPSs implies robust stability, but also presents criterions in terms of linear matrix inequalities to test the (affine) generalized quadratic stability based on time-varying parameter-dependent Lyapunov function. Finally, a numerical example presents the effectiveness of the proposed method.