Robust Filtering of 2-D Uncertain State-Delayed Systems

Abstract

This chapter is concerned with the robust $\mathcal {H}_{\infty }$ filtering for uncertain 2-D discrete systems with time-delay in its states. The mathematical model of the 2-D systems is established in terms of the well-known FMLSS model incorporating time delays. We aim at designing a filter that guarantees the asymptotic stability of the filtering error system while keeping the prescribed $\mathcal {H}_{\infty }$ disturbance attenuation performance. The existence conditions of the desired filters are first established in terms of LMIs, and the corresponding filter design is converted into a convex optimization problem. Furthermore, the obtained results are extended to some more general cases where the system matrices also contain uncertain parameters. Most frequently used descriptions for the parameter uncertainties, including polytopic and norm-bounded characterizations, are taken into consideration.