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Stability of systems with state-dependent and random delays. (English) Zbl 1010.34078
The author focusses on dynamical systems with a delay or time lag varying in time. By Lyapunov-Krasovskii theory, sufficient conditions for the global asymptotic stability are derived. In the first part, the case of stochastic delay differential equations with Brownian motion as driving process and a randomly varying time delay independent of Brownian motion (but Markovian) is considered. Secondly, linear deterministic systems, but with nonlinear state-dependent delay, are investigated, and an oscillator system with friction and state-dependent delay is studied in more detail. One is lead to consider a so-called delay algebraic Riccati equation in order to derive stability.

MSC:
34K50 Stochastic functional-differential equations
34K20 Stability theory of functional-differential equations
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