Robust energy-to-peak filtering for uncertain discretetime state-delayed systems: Delay independent and dependent approaches

This paper deals with the robust l_∞-l_∞ filtering problem for discrete-time systems with multiple delays in the state and uncertain parameters residing in a polytope. We focus on the design of robust full order and reduced order filters, which can guarantee a prescribed energy-to-peak disturbance attenuation level. Two approaches are presented to solve the filtering problem: delay-independent (suitable for systems with unknown delay bounds) and delay-dependent (suitable for systems with known delay bounds). 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. This greatly reduces the conservatism of the quadratic framework.