Design of reduced-order ℓ₂-ℓ_∞ filter design for singular discrete-time systems using strict linear matrix inequalities

In this study, the problem of designing regular robust ℓ₂- ℓ_∞ filter for a class of linear singular discrete-time systems with norm-bounded uncertainties is investigated. A class of regular linear filters is fully analysed, then necessary and sufficient conditions of robust admissibility are established. Guaranteed ℓ₂- ℓ_∞ performance of the filtered system is provided and expressed in terms of the solution of strict linear matrix inequalities (LMIs). The cases of full- and zeroth-order realisable filter are derived as limiting cases of design. Numerical examples are worked out to illustrate the theoretical development.