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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.

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
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