Mainly addressed in this paper is the stability problem of continuous-time switched cascade nonlinear systems with time-varying delays. A robust convergence property is proved first: If a nominal switched nonlinear system with delays is asymptotically stable, then trajectories of corresponding perturbed system asymptotically approach origin provided that the perturbation can be upper bounded by a function exponentially decaying to zero. Applying this property and assuming that a cascade system consists of two separate systems, it is shown that a switched cascade nonlinear system is asymptotically stable if one separate system is exponentially stable and the other one is asymptotically stable. Since the considered switching signals have a uniform property and thus include most switching signals frequently encountered, our results are valid for a wide range of switched cascade systems.
Citation: Xingwen Liu, Shouming Zhong. Stability analysis of delayed switched cascade nonlinear systems with uniform switching signals[J]. Mathematical Modelling and Control, 2021, 1(2): 90-101. doi: 10.3934/mmc.2021007
Mainly addressed in this paper is the stability problem of continuous-time switched cascade nonlinear systems with time-varying delays. A robust convergence property is proved first: If a nominal switched nonlinear system with delays is asymptotically stable, then trajectories of corresponding perturbed system asymptotically approach origin provided that the perturbation can be upper bounded by a function exponentially decaying to zero. Applying this property and assuming that a cascade system consists of two separate systems, it is shown that a switched cascade nonlinear system is asymptotically stable if one separate system is exponentially stable and the other one is asymptotically stable. Since the considered switching signals have a uniform property and thus include most switching signals frequently encountered, our results are valid for a wide range of switched cascade systems.
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