ON THE METHOD OF CONE-VALUED LYAPUNOV FUNCTIONS

作者: V. Lakshmikantham , S. Leela

DOI: 10.1016/B978-0-12-434150-0.50024-2

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摘要: Publisher Summary This chapter describes the method of cone-valued Lyapunov functions. The technique employing vector functions and theory differential inequalities offers a great deal flexibility in studying nonlinear systems. However, for success this method, it is required that comparison system be quasimonotone nondecreasing. In case linear system, requirement implies nondiagonal elements matrix all nonnegative. limitation application potential general effective because fact systems may have desired property like positivity or stability solutions without being quasimonotone. It was observed difficulty choice cone relative to namely Rn+, nonnegative Rn possible approach overcome choose an appropriate other than Rn+. presents idea by developing through cones, shown useful tool applications.

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