A nested Matrosov theorem and persistency of excitation for uniform convergence in stable nonautonomous systems

被引:127
作者
Loría, A
Panteley, E
Popovic, D
Teel, AR
机构
[1] CNRS, Signaux & Syst Lab, UMR 8506, F-91192 Gif Sur Yvette, France
[2] United Technol Res Ctr, E Hartford, CT 06108 USA
[3] Univ Calif Santa Barbara, Dept Elect & Comp Engn, Ctr Control Engn & Comp, Santa Barbara, CA 93106 USA
基金
美国国家科学基金会;
关键词
Matrosov theorem; nonholonomic systems; time-varying systems; uniform stability;
D O I
10.1109/TAC.2004.841939
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
A new infinitesimal sufficient condition is given for uniform global asymptotic stability (UGAS) for time-varying nonlinear systems. It is used to show that a certain relaxed persistency of excitation condition, called uniform delta-persistency of excitation (Udelta-PE), is sufficient for uniform global asymptotic stability in certain situations. Udelta-PE of the right-hand side of a time-varying differential equation is also shown to be necessary under a uniform Lipschitz condition. The infinitesimal sufficient condition for UGAS involves the inner products of the flow field with the gradients of a finite number of possibly sign-indefinite, locally Lipschitz Lyapunov-like functions. These inner products are supposed to be bounded by functions that have a certain nested, or triangular, negative semidefinite structure. This idea is reminiscent of a previous idea of Matrosov who supplemented a Lyapunov function having a negative semidefinite derivative with an additional function having a derivative that is "definitely nonzero" where the derivative of the Lyapunov function is zero. For this reason, we call the main result a nested Matrosov theorem. The utility of our results on stability analysis is illustrated through the well-known case-study of the nonholonomic integrator.
引用
收藏
页码:183 / 198
页数:16
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