Robust Filtering with l₂-l_∞ Performance for Uncertain Discrete-Time Systems with Multiple State Delays

This paper deals with the robust l₂-l_∞ filtering problem for discrete-time systems with multiple delays in the state and uncertain parameters residing in a polytope. Attention is focused on the design of robust full order and reduced order filters guaranteeing a prescribed energy-to-peak disturbance attenuation level. Sufficient conditions for the existence of admissible filters are formulated in terms of linear matrix inequalities, upon which both the delay-independent and dependent filtering problems are cast into convex optimization problems. These two approaches also incorporate a new parameter-dependent stability result into the filter designs, which greatly reduces the conservatism of the quadratic framework. The proposed filter design methods are applicable to systems either with or without known delay bounds. Illustrative examples are provided to demonstrate the effectiveness of the proposed filter design methodologies.