Class- $$\mathcal{K}$$ Function Bounds for Positive Definite Functions on Compact Sets
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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.
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Keywords
Comparison functions, nonlinear systems, positive definite functions, stability analysis
Journal Title
International Journal of Control, Automation and Systems
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Journal ISSN
1598-6446
2005-4092
2005-4092
Volume Title
17
Publisher
Springer Science and Business Media LLC
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