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Stability for a class of nonlinear time-delay systems via Hamiltonian functional method

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Abstract

This paper investigates the stability of a class of nonlinear time-delay systems via Hamiltonian functional method, and proposes a number of new results on generalized Hamiltonian realization (GHR) and stability analysis for this class of systems. Firstly, the concept of GHR of general nonlinear time-delay systems is proposed, and several new GHR methods are given. Then, based on the new GHR methods obtained, the stability of time-delay systems is investigated, and several delay-dependent sufficient conditions in term of matrix inequalities are derived for the stability analysis by constructing suitable Lyapunov-Krasovskii (L-K) functionals. Finally, an illustrative example shows that the results obtained in this paper have less conservatism, and work very well in the stability analysis of some nonlinear time-delay Hamiltonian systems.

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Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, Jinan, 250061, China

    RenMing Yang & YuZhen Wang

  2. Shandong Jiaotong University, Jinan, 250023, China

    RenMing Yang

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  1. RenMing Yang
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  2. YuZhen Wang
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Correspondence to RenMing Yang or YuZhen Wang.

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Yang, R., Wang, Y. Stability for a class of nonlinear time-delay systems via Hamiltonian functional method. Sci. China Inf. Sci. 55, 1218–1228 (2012). https://doi.org/10.1007/s11432-012-4573-z

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  • DOI: https://doi.org/10.1007/s11432-012-4573-z

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