Set-Invariant Estimators for Multiple-Output Discrete-Time Systems

A new technique for the design of full-order state observers with limitation of the estimation error has been recently proposed, based on the concept of set-invariance. However, such a technique was limited to single-output linear systems. In this paper, the design of set-invariant estimators is extended to multiple-output linear discrete-time systems subject to bounded disturbances. Based on multiparametric linear programming concepts, necessary and sufficient conditions are established under which a given polyhedral set defined on the estimation error space is invariant, in the sense that the error trajectory can be kept in this set by means of a suitable output injection. Moreover, three algorithms are proposed for the computation of an invariant polyhedron which bounds the trajectory of the estimation error. Important issues such as the computation of the output injection law and the convergence of the proposed algorithms are discussed as well. Numerical examples illustrate the proposed technique