A delay-dependent approach to robust H∞ filtering for uncertain discrete-time state-delayed systems

A delay-dependent approach to robust H_∞ filtering is proposed for linear discrete-time uncertain systems with multiple delays in the state. The uncertain parameters are supposed to reside in a polytope and the attention is focused on the design of robust filters guaranteeing a prescribed H_∞ noise attenuation level. The proposed filter design methodology incorporates some recently appeared results, such as Moon´s new version of the upper bound for the inner product of two vectors and de Oliveira´s idea of parameter-dependent stability, which greatly reduce the overdesign introduced in the derivation process. In addition to the full-order filtering problem, the challenging reduced-order case is also addressed by using different linearization procedures. Both full- and reduced-order filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities, which can be solved via efficient interior-point algorithms. Numerical examples have been presented to illustrate the feasibility and advantages of the proposed methodologies.