Robust filtering for discrete time-delay systems

This chapter focuses on the design of robust H-infinity filters for discrete-time systems with polytopic uncertainty and a delay in the state. Based on a discrete-time Lyapunov-Krasovskii functional, a sufficient parameter-dependent linear matrix inequality (LMI) condition is established for the H-infinity filtering performance. Then a new performance analysis condition is obtained through introducing slack matrices, so as to decouple the product of the Lyapunov matrices and system matrices. Based on the performance analysis condition, a sufficient delay-dependent condition is derived for the existence of robust H-infinity filters for uncertain discrete time-delay systems, and is further transformed into linear matrix inequality conditions by applying the polynomially parameter-dependent idea. Several numerical examples are finally employed to show the effectiveness of the robust filter design method in this chapter for uncertain discrete time-delay systems.