A Mean Square Stability Test for Markovian Jump Linear Systems

C. Nespoli, J.B.R. do Val

Abstract


This paper proposes a test for the mean square stability problem for discrete-time linear systems subject to random jumps in the parameters, described by an underlying finite-state Markov chain. In the model studied, the horizon of the problem is given by a stopping time , associated with the occurrence of a crucial failure after which the system is brought to a halt for maintenance. The usual stochastic stability concepts and associated results are not indicated, since they are tailored to purely infinite horizon problems. Using the concept named stochastic -stability, equivalent conditions to ensure the stochastic stability of the system until the occurrence of is obtained. These conditions lead to a test that benefits from the chain structure for proposing a simpler decomposition algorithm for the mean square stability verification for infinite horizon problems.

References


[1] E. C¸ inlar, “Introduction to Stochastic Processes”, Prentice-Hall, 1975.

O.L.V. Costa, M.D. Fragoso, R.P. Marques, “Discrete-Time Markov Jump Linear Systems”, Probability and its Aplications, Springer, New York, 2005.

O.L.V. Costa, M.D. Fragoso, Stability results for discrete-time linear systems with Markovian jumping parameters, Journal of Mathematical Analysis and Applications, 179 (1993), 154-178.

J.B.R. do Val, C. Nespoli, Y.R.Z. C´aceres, Stochastic stability for Markovian jump linear systems associated with a finite number of jump times, Journal of Mathematical Analysis and Applications, 285, No. 3 (2003), 551-563.

G.H. Golub, C.F. Van Loan, “Matrix Computation”, John Hopkins Univ. Press, 1996.

Y. Ji, H.J. Chizeck, K.A. Loparo, Stability and control of discrete-time jump linear systems, Control Theory and Advanced Technology, 7 (1991), 247-270.

Y. Ji, H.J. Chizeck, Jump linear quadratic Gaussian control: Steady-state solution and testable conditions, Control Theory and Advanced Technology, 6, No. 3 (1990), 289-319.

K. Zhou, J.C. Doyle, K. Glover, “Robust and Optimal Control”, Prentice-Hall, 1996.




DOI: https://doi.org/10.5540/tema.2008.09.02.0299

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TEMA - Trends in Applied and Computational Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)
ISSN: 1677-1966  (print version),  2179-8451  (online version)

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