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On boundedness and attractiveness of nonlinear switched delay systems. (English) Zbl 1470.34176

Summary: This paper is concerned with the boundedness and attractiveness of nonlinear switched delay systems whose subsystems have different equilibria. Some sufficient conditions which can guarantee the system’s boundedness are obtained. In addition, we work out the region where the solution will remain and furthermore the relationship between the initial function and the bounded region. Based on the new concept of attractor with switching laws, we show that the nonlinear switched delay system is attractive and then obtain the attractive region.

MSC:

34K12 Growth, boundedness, comparison of solutions to functional-differential equations
34K20 Stability theory of functional-differential equations
34K34 Hybrid systems of functional-differential equations
93D15 Stabilization of systems by feedback
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