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Exponential stability of linear distributed parameter switched systems with time-delay

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Abstract

In this paper, the exponential stability analysis for ODE switched systems with time delay is extended to distributed parameter switched systems (DPSS) in Hilbert space. For a given family of exponential stable subsystems, this paper focuses on finding conditions to guarantee the overall DPSS’ exponential stability. Based on semigroup theory, by applying piecewise Lyapunov-Krasovskii functionals method incorporated average dwell time approach, sufficient conditions for exponential stability are derived. These conditions are given in the form of linear operator inequalities (LOIs) where the decision variables are operators in Hilbert space, and the stability properties depend on switching rule. Being applied to heat switched propagation equations, these LOIs are reduced to standard Linear Matrix Inequalities (LMIs). Finally, a numerical example is given to illustrate the effectiveness of the proposed result.

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Authors and Affiliations

  1. The School of Automation and Key Laboratory of Measurement and Control of Complex Systems of Engineering, Southeast University, Nanjing, 210096, China

    Leping Bao & Shumin Fei

  2. The School of Mechanical and Electric Engineering, Soochow University, Suzhou, 215021, China

    Lei Yu

Authors
  1. Leping Bao
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  2. Shumin Fei
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  3. Lei Yu
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Corresponding author

Correspondence to Leping Bao.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 61273119, 61104068, 61374038, and the Natural Science Foundation of Jiangsu Province of China under Grant No. BK2011253.

This paper was recommended for publication by Editor FENG Dexing.

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Bao, L., Fei, S. & Yu, L. Exponential stability of linear distributed parameter switched systems with time-delay. J Syst Sci Complex 27, 263–275 (2014). https://doi.org/10.1007/s11424-014-3070-4

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  • DOI: https://doi.org/10.1007/s11424-014-3070-4

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