Reduced-order H-infinity filter for singular discrete-time using strict LMIs

In this paper, the problem of designing reduced-order realizable H _∞ filter for a class of linear singular discrete-time systems with norm-bounded uncertainties is investigated. The design objective of the robust reduced-order filter is to guarantee a prescribed upper bound on an H_∞performance is attained for all possible energybounded input disturbances, for all admissible uncertainties and which can be implemented on-line with less computational complexity. A class of reduced-order and regular linear filters is fully analyzed, then necessary and sufficient conditions for the H_∞ performance of the filtered system are provided. It is established that the solution to the filtering design problem can be cast in the format of strict linear matrix inequalities (LMIs). Several special cases are deduced. A detailed numerical example is worked out to illustrate the theoretical developments.