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Almost sure and moments stability of jump linear systems. (English) Zbl 0672.93073
Summary: The stability of piecewise deterministic linear systems driven by an underlying finite Markov chain is analyzed. Necessary and sufficient conditions for moment stability are obtained by means of an explicit formula for the corresponding Liapunov exponent. The relationship between almost sure and moment stability is elucidated, revealing the possible occurrence of high order moment instability and large deviations from a stable sample path behavior.

93E15 Stochastic stability in control theory
93E03 Stochastic systems in control theory (general)
Full Text: DOI
[1] Arnold, L., A formula connecting sample path and moment stability of linear stochastic systems, SIAM J. appl. math., 44, 793-802, (1984) · Zbl 0561.93063
[2] Liapunov exponents, ()
[3] Blankenship, G., Stability of linear differential equations with random coefficients, IEEE trans. automat. control, 22, 834-838, (1977) · Zbl 0362.93033
[4] Chang, K.C.; Bar-Shalom, Y., Distributed multiple model estimation, (), 797-802
[5] Hopkins, W.E., Optimal stabilization of families of linear stochastic differential equations with jump coefficients and multiplicative noises, SIAM J. control optim., (1988), to appear
[6] Ladde, G.S.; Siljak, D.D., Multiplex control systems: stochastic stability and dynamic reliability, Internat. J. control, 38, 515-524, (1983) · Zbl 0524.93067
[7] Li, C.W.; Blankenship, G.L., Almost sure stability of linear stochastic systems with Poisson process coefficients, SIAM J. appl. math., 46, 875-911, (1986) · Zbl 0613.60053
[8] Loparo, K.A., Stochastic stability of coupled linear systems: a survey of methods and results, Stochastic analysis appl., 2, 193-228, (1984) · Zbl 0542.93070
[9] K.A. Loparo and G.L. Blankenship, Almost sure instability of a class of linear stochastic systems with jump process coefficients, in [2], 160-228. · Zbl 0599.93066
[10] Marcus, S.I., Modeling and analysis of stochastic differential equations driven by point processes, IEEE trans. inform. theory, 24, 164-172, (1978) · Zbl 0372.60084
[11] Mariton, M.; Bertrand, P., Comportement asymptotique de la commande pour LES systemes lineaires a sauts markoviens, C.R. acad. sci. Paris, Sér. I, 301, 683-686, (1985) · Zbl 0585.93065
[12] Mariton, M.; Bertrand, P., Improved multiplex control: dynamic reliability and stochastic optimality, Internat. J. control, 44, 219-234, (1986) · Zbl 0598.93067
[13] Mariton, M.; Bertrand, P., Asymptotic behavior of jump linear quadratic systems in continuous time, (), 483-494
[14] Sworder, D.D.; Chou, S.D., A survey of design methods for random parameter systems, (), 894-899
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