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

✍ Scribed by Eduardo F. Costa; João B.R. do Val

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
135 KB
Volume
44
Category
Article
ISSN
0167-6911

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✦ Synopsis

This paper presents a new detectability concept for discrete-time Markov jump linear systems with ÿnite Markov state, which generalizes the MS-detectability concept found in the literature. The new sense of detectability 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 detectability based on a coupled matrix equation is derived from the deÿnition, and a test for observability is presented, which can be performed in a ÿnite 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.

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