Robust H∞ filter design for uncertain discrete-time state-delayed systems: an LMI approach

The problem of robust H_∞ filtering for discrete-time uncertain linear systems with multiple state delays is addressed. The uncertain parameters are supposed to belong to a given convex bounded polyhedral domain. Sufficient conditions for the existence of a stable linear filter assuring stability and a prescribed H_∞ performance for the filtering error system for all allowed uncertainties are established in terms of linear matrix inequalities. Efficient numerical algorithms can be used to solve the problem, as illustrated via an example