Almost sure and moments stability of jump linear systems.

*(English)*Zbl 0672.93073Summary: 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.

##### MSC:

93E15 | Stochastic stability in control theory |

93E03 | Stochastic systems in control theory (general) |

##### Keywords:

stability of piecewise deterministic linear systems; finite Markov chain; moment stability; Liapunov exponent; relationship between almost sure and moment stability; high order moment instability; large deviations from a stable sample path behavior
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\textit{M. Mariton}, Syst. Control Lett. 11, No. 5, 393--397 (1988; Zbl 0672.93073)

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##### References:

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