Observability and Dead-Beat Observers for Discrete-Time Linear Multivariable Systems with Unknown Inputs

Abstract

New concepts for an unknown input unobservable subspacs and an unknown input oservability for discrete-time linear multivariable systems are introduced. These new concepts, namely (r, s) unobservable subspace and (r, s; K) observability, are extensions of conventional one. Algorithms for obtaining the (r, s) unobservable subspace are presented using both matrix and vector-space (geometrical) operations. Necessary and sufficient conditions for (r, s; K) observability are also derived and the relation between this and the canonical form is clarified. It is also shown that there exists a dead-beat K-observer, of which the output coincides with the partial state of the system Kx (i) after some time, if and only if the system is (r, s: K) observable for some integers r snd s. An algorithm for constructing this observer is developed in a simple matrix form.