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Exponential Stability of Switched Systems with Unstable Subsystems: A Mode-Dependent Average Dwell Time Approach

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Abstract

This article studies the exponential stability of switched systems with unstable subsystems. By using the multiple Lyapunov function (MLF) method combined with mode-dependent average dwell time (MDADT) techniques, less conservative exponential stability conditions are derived in terms of a set of solvable linear matrix inequalities (LMIs). Compared to the existing results, unstable subsystems are considered based on MDADT in this paper. It is revealed that switched systems can be exponentially stable under slow switching schemes and also in the presence of fast switching of unstable subsystems. A numerical example and its simulations are also given to verify the effectiveness of the proposed method.

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Notes

  1. “Switching in” means the moment when the switched system just enters a certain subsystem. Here, we use V i (x(t 1)),V i (x(t 2)),…,V i (x(t k )),V i (x(t k+1)),… to represent the switching in instant of the ith subsystem.

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Acknowledgements

The work was supported in part by the National Natural Science Foundation of China (Grant nos. 61174137 and 61104064), the NSF of Jiang Su Province (Grant no. BK2010493), and a grant from the China Postdoctoral Science Foundation funded project 2012M510135.

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Authors and Affiliations

  1. Centre for Nonlinear and Complex Systems, School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, P.R. China

    Dehua Xie, Hongyu Zhang, Hongbin Zhang & Bo Wang

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  1. Dehua Xie
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  2. Hongyu Zhang
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  3. Hongbin Zhang
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  4. Bo Wang
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Correspondence to Hongbin Zhang.

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Xie, D., Zhang, H., Zhang, H. et al. Exponential Stability of Switched Systems with Unstable Subsystems: A Mode-Dependent Average Dwell Time Approach. Circuits Syst Signal Process 32, 3093–3105 (2013). https://doi.org/10.1007/s00034-013-9601-8

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  • DOI: https://doi.org/10.1007/s00034-013-9601-8

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