Regular Papers
International Journal of Control, Automation and Systems 2019; 17(10): 2550-2555
Published online July 26, 2019
https://doi.org/10.1007/s12555-018-0782-6
© The International Journal of Control, Automation, and Systems
Class-K Function Bounds for Positive Definite Functions on Compact Sets
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.
Keywords Comparison functions, nonlinear systems, positive definite functions, stability analysis.
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Regular Papers
International Journal of Control, Automation and Systems 2019; 17(10): 2550-2555
Published online October 1, 2019 https://doi.org/10.1007/s12555-018-0782-6
Copyright © The International Journal of Control, Automation, and Systems.
Class-K Function Bounds for Positive Definite Functions on Compact Sets
Seungjoon Lee, Jin Gyu Lee, and Hongkeun Kim*
Korea University of Technology and Education
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.
Keywords: Comparison functions, nonlinear systems, positive definite functions, stability analysis.
Vol. 23, No. 3, pp. 683~972
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