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On stability of linear and weakly nonlinear switched systems with time delay. (English) Zbl 1187.34067

Summary: This paper studies time-delayed switched systems that include both stable and unstable modes. By using multiple Lyapunov-functions technique and a dwell-time approach, several criteria on exponential stability for both linear and nonlinear systems are established. It is shown that by suitably controlling the switching between the stable and unstable modes, exponential stabilization of the switched system can be achieved. Some examples and numerical simulations are provided to illustrate our results.

MSC:

34D20 Stability of solutions to ordinary differential equations
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