On the detectability and observability of discrete-time Markov jump linear systems

This paper presents a new delectability concept for discrete-time Markov jump linear systems with finite Markov state, which generalizes the MS-detectability concept found in the literature. The new sense of delectability can similarly assure that the solution of the coupled algebraic Riccati equation associated to the quadratic control problem is a stabilizing solution. In addition, the paper introduces a related observability concept that also generalizes previous concepts. A test for delectability based on a coupled matrix equation is derived from the definition, and a test for observability is presented, which can be performed in a finite number of steps. The results are illustrated by examples, including one that shows that a system may be detectable in the new sense but not in the MS sense. (C) 2001 Elsevier Science B.V. All rights reserved.