Impact of average-dwell-time characterizations for switched nonlinear systems on complex systems control

Dimirovski, Georgi and Wang, Jiqiang and Yue, Hong and Stefanovski, Jovan; Kondratenko, Yuriy P. and Chikrii, Arkadii A. and Gubarev, Vyacheslav F. and Kacprzyk, Janusz, eds. (2019) Impact of average-dwell-time characterizations for switched nonlinear systems on complex systems control. In: Advanced Control Techniques in Complex Engineering Systems. Studies in Systems, Decision and Control . Springer, Cham, Switzerland, pp. 35-50. ISBN 9783030219260 (https://doi.org/10.1007/978-3-030-21927-7_2)

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Abstract

It is well known, present day theory of switched systems is largely based on assuming certain small but finite time interval termed average dwell time. Thus it appears dominantly characterized by some slow switching condition with the average dwell time satisfying a certain lower bound, which implies a constraint nonetheless. In cases of nonlinear systems, there may well appear certain non-expected complexity phenomena of particularly different nature when switching becomes no longer useful. A fast switching condition with average the dwell time satisfying an upper bound is explored and established. A comparison analysis of these innovated characterizations via slightly different overview yielded new results on the transient behaviour of switched nonlinear systems, while preserving the system stability. The approach of multiple Lyapunov functions is used in current analysis and the switched systems framework is believed to be extended slightly. Thus some new insight into the underlying, switching caused, system’s complexities has been achieved.

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