Krasovskii and Razumikhin stability theorems for stochastic switched nonlinear time-delay systems. (English) Zbl 1410.34246
Summary: This paper studies stability properties of stochastic switched nonlinear time-delay systems. The stability analysis is based on two extensions of the Lyapunov-based method: the Krasovskii approach and the Razumikhin approach. In terms of the Krasovskii approach, Krasovskii-type stability conditions are derived based on Lyapunov-Krasovskii functions and average dwell-time condition. In terms of the Razumikhin approach, Razumikhin-type stability conditions are obtained via Lyapunov-Razumikhin functions, the small gain condition, and the fixed dwell-time condition. Furthermore, as a widespread phenomenon in switched systems, the asynchronous switching case is studied. Both Krasovskii-type and Razumikhin-type stability conditions are established for the asynchronous switching case. Finally, the developed results are illustrated via two examples from the mechanical rotational cutting process and networked switched control systems.
MSC:
| 34K50 | Stochastic functional-differential equations |
| 34K20 | Stability theory of functional-differential equations |
| 34K34 | Hybrid systems of functional-differential equations |
| 93E15 | Stochastic stability in control theory |
| 34A36 | Discontinuous ordinary differential equations |
Keywords:
Lyapunov-Krasovskii function; Lyapunov-Razumikhin function; time delay; stochastic switched systems; asynchronous switching; stochastic stabilityReferences:
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