Brief paper: On almost sure stability of continuous-time Markov jump linear systems

Authors:
P. Bolzern;P. Colaneri;G. De Nicolao
Affiliations:
Dipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy;Dipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy;Dipartimento di Informatica e Sistemistica, Universití di Pavia, Via Ferrata 1, 27100 Pavia, Italy
Venue:
Automatica (Journal of IFAC)
Year:
2006

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Abstract

In this paper, we study the almost sure stability of continuous-time jump linear systems with a finite-state Markov form process. A sufficient condition for almost sure stability is derived that refers to the statistics of the transition matrix over m switches. It is shown that, if the system is exponentially almost sure stable, there exists a finite m such that the criterion is satisfied. In order to evaluate the expected value appearing in the condition, an efficient Monte Carlo algorithm is worked out.