Filter Design for Discrete-Time Linear Descriptor Systems

Abstract

System state estimation plays an important role in control, monitoring and fault detection of dynamical processes, not excluding the problem of state filtering for descriptor systems. In the context of $H_{\infty}$ filtering, the paper subject is design of observers for discrete-time linear descriptor systems. Reflecting conditions for admissibility related to this class of systems, convex optimization task is proposed for descriptor filter design, ensuring filter gain norm. The proposed design formulation is based on generalized Lyapunov function and considers a filter descriptor structure of full-order. Numerical example is presented to show the effectiveness of the proposed filtering scheme.