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Class-K Function Bounds for Positive Definite Functions on Compact Sets

Seungjoon Lee, Jin Gyu Lee, and Hongkeun Kim*
International Journal of Control, Automation, and Systems, vol. 17, no. 10, pp.2550-2555, 2019

Abstract : This technical note focuses on positive definite functions defined on compact sets which contain the origin in their interior. It provides a class-K function bounding inequality for the given positive definite function which is satisfied for its entire domain of definition. An application of the result is also given to analyze the stability of perturbed nonlinear systems whose nominal parts contain an asymptotically stable equilibrium point at the origin.

Keyword : Comparison functions, nonlinear systems, positive definite functions, stability analysis.

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