@article{Liu2021, 
author = {Xingwen Liu and Shouming Zhong},
title = {Stability analysis of delayed switched cascade nonlinear systems with uniform switching signals},
year = {2021},
journal = {Mathematical Modelling and Control},
volume = {1},
number = {2},
pages = {90-101},
keywords = {stability, switched systems, delays, cascade systems, uniform switching signals},
url = {https://www.sciopen.com/article/10.3934/mmc.2021007},
doi = {10.3934/mmc.2021007},
abstract = {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.}
}