Dead-Beat Functional Observers for Discrete-Time LPV Systems With Unknown Inputs

This technical note deals with functional observers for discrete-time linear parameter varying (LPV) systems. More specifically, dead-beat observers for reconstructing linear combinations of the state are proposed. The system inputs are assumed to be unknown and the observers reduce to functions of the output over a finite number of time-steps. The existence of such observers is proven by resorting to the notion of inverse system together with the concepts of maximal robust invariant subspaces and nilpotent semigroups. A constructive approach to derive the explicit equations of the observer is provided. An example illustrates the efficiency and the computational aspects of the method.