# Class-$$\mathcal{K}$$ Function Bounds for Positive Definite Functions on Compact Sets

Lee, S and Lee, JG and Kim, H (2019) Class-$$\mathcal{K}$$ Function Bounds for Positive Definite Functions on Compact Sets. International Journal of Control, Automation and Systems, 17. pp. 2550-2555. ISSN 1598-6446

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## Abstract

This technical note focuses on positive definite functions defined on compact sets which contain the origin in their interior. It provides a class- 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.

Item Type: Article UNSPECIFIED Div F > Control Cron Job 19 Oct 2020 20:04 29 Jul 2021 05:13 10.1007/s12555-018-0782-6