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Relaxed persistency of excitation for uniform asymptotic stability. (English) Zbl 1032.93070

The authors of this paper propose a relaxed definition for persistence of excitation (uniform persistence of excitation), a property crucial for some stability analyses of parameter identification algorithms and adaptive control systems. The relaxed definition is used to establish uniform global asymptotic stability and uniform local exponential stability for a large class of nonlinear, time varying systems.
The relaxed definition of persistence of excitation that the authors propose is conceptually equivalent to the definition proposed by Loría et al. in a 1999 paper, but the newer definition is easier to verify. The authors claim that the new definition is useful for the stability analysis of nonlinear systems arising in nonlinear adaptive control, stabilization of nonholonomic systems, and tracking control.
The authors’ work is motivated in part by the need for stability analysis methods when classical Lyapunov theory is too restrictive.

MSC:

93D20 Asymptotic stability in control theory
93D21 Adaptive or robust stabilization
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