A Mean Square Stability Test for Markovian Jump Linear Systems

Authors

  • C. Nespoli
  • J.B.R. do Val

DOI:

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

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

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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.

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Published

2008-06-01

How to Cite

Nespoli, C., & do Val, J. (2008). A Mean Square Stability Test for Markovian Jump Linear Systems. Trends in Computational and Applied Mathematics, 9(2), 299–310. https://doi.org/10.5540/tema.2008.09.02.0299

Issue

Vol. 9 No. 2 (2008)

Section

Original Article

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