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**Construction of Lyapunov functionals for stochastic hereditary systems: A survey of some recent results.**
*(English)*
Zbl 1029.93057

Stochastic discrete-time systems with multiple delays are considered. A procedure for Lyapunov function construction is given for such systems. This procedure is applied to linear systems with constant coefficients, with monotone coefficients, with time-varying delays, and with discrete Volterra equations of the second type. Then, continuous-time versions of these results are presented. Many illustrative examples are also incorporated into the paper.

Reviewer: Edwin Engin Yaz (Fayetteville)

### MSC:

93D30 | Lyapunov and storage functions |

93E15 | Stochastic stability in control theory |

93C55 | Discrete-time control/observation systems |

93C23 | Control/observation systems governed by functional-differential equations |

### Keywords:

Lyapunov stability; stochastic stability; discrete-time systems; systems governed by functional-differential equations; time-varying systems; Lyapunov function; time-varying delays; Volterra equations
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\textit{V. Kolmanovskii} and \textit{L. Shaikhet}, Math. Comput. Modelling 36, No. 6, 691--716 (2002; Zbl 1029.93057)

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### References:

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