On Delay-Dependent Global Asymptotic Stability for Pendulum-Like Systems

P. L. Lu () and Y. Yang
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P. L. Lu: Beijing Institute of Technology
Y. Yang: Peking University

Journal of Optimization Theory and Applications, 2009, vol. 143, issue 2, No 5, 295-308

Abstract: Abstract This paper deals with global asymptotic stability for the delayed nonlinear pendulum-like systems with polytopic uncertainties. The delay-dependent criteria, guaranteeing the global asymptotic stability for the pendulum-like systems with state delay for the first time, are established in terms of linear matrix inequalities (LMIs) which can be checked by resorting to recently developed algorithms solving LMIs. Furthermore, based on the derived delay-dependent global asymptotic stability results, LMI characterizations are developed to ensure the robust global asymptotic stability for delayed pendulum-like systems under convex polytopic uncertainties. The new extended LMIs do not involve the product of the Lyapunov matrix and the system matrices. It enables one to check the global asymptotic stability by using parameter-dependent Lyapunov methods. Finally, a concrete application to phase-locked loop (PLL) shows the validity of the proposed approach.

Keywords: Pendulum-like systems; Time delay; Global asymptotic stability; Linear matrix inequalities; Polytopic uncertainties (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/s10957-009-9578-4

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