Robust ℋ∞ filtering for uncertain discrete-time state-delayed systems

This paper addresses the problem of robust ℋ_∞ filtering for linear discrete-time systems subject to parameter uncertainties in the system state-space model and with multiple time delays in the state variables. The uncertain parameters are supposed to belong to a given convex bounded polyhedral domain. A methodology is developed to design a stable linear filter that assures asymptotic stability and a prescribed ℋ_∞ performance for the filtering error, irrespective of the uncertainty and the time delays. The proposed design is given in terms of linear matrix inequalities, which has the advantage in that it can be implemented numerically very efficiently