### Mathematical Modelling and Control

2021, Issue 2: 90-101. doi: 10.3934/mmc.2021007
Research article

# Stability analysis of delayed switched cascade nonlinear systems with uniform switching signals

• Received: 10 April 2021 Accepted: 25 May 2021 Published: 22 June 2021
• 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

### Related Papers:

• 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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• © 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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沈阳化工大学材料科学与工程学院 沈阳 110142

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