Volume 28, 2022
|Number of page(s)||23|
|Published online||17 February 2022|
Necessary and sufficient conditions for the nonincrease of scalar functions along solutions to constrained differential inclusions*
University Grenoble Alpes, CNRS, Grenoble INP, Gipsa lab,
2 Department of Electrical, Electronic, and Information Engineering, University of Bologna, Italy.
3 Department of Electrical & Computer Engineering, University of California Santa Cruz, CA, USA.
** Corresponding author: firstname.lastname@example.org
Accepted: 26 January 2022
In this paper, we propose necessary and sufficient conditions for a scalar function to be nonincreasing along solutions to general differential inclusions with state constraints. The problem of determining if a function is nonincreasing appears in the study of stability and safety, typically using Lyapunov and barrier functions, respectively. The results in this paper present infinitesimal conditions that do not require any knowledge about the solutions to the system. Results under different regularity properties of the considered scalar function are provided. This includes when the scalar function is lower semicontinuous, locally Lipschitz and regular, or continuously differentiable.
Mathematics Subject Classification: 93A10 / 26B05
Key words: Constrained systems / Differential inclusions / Nonincreasing functions / Lyapunov-like functions
© The authors. Published by EDP Sciences, SMAI 2022
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