Robust non-Zenoness of piecewise analytic systems with applications to complementarity systems

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Robust_non_Zenoness_of_piecewise_analyti.pdf (231.07 KB)

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https://ieeexplore.ieee.org/document/5531225

Permanent Link

https://doi.org/10.1109/ACC.2010.5531225
 http://hdl.handle.net/11603/35758

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UMBC Faculty Collection
UMBC Mathematics and Statistics Department

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Author/Creator ORCID

https://orcid.org/0000-0003-2172-4182

Date

2010-07-29

Type of Work

conference papers and proceedings
preprints
Text

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Program

Citation of Original Publication

Shen, Jinglai. “Robust Non-Zenoness of Piecewise Analytic Systems with Applications to Complementarity Systems.” In Proceedings of the 2010 American Control Conference, 148–53, 2010. https://doi.org/10.1109/ACC.2010.5531225.

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Subjects

Analytical models
Computational modeling
Constraint optimization
Control systems
Nonlinear dynamical systems
Performance analysis
Robust control
Robustness
Uncertain systems
Uncertainty

Abstract

This paper addresses non-Zenoness of a class of Lipschitz piecewise analytic systems subject to state perturbations and parameter uncertainties, motivated by sensitivity analysis of such systems. Specifically, the existence of uniform bounds on the number of mode switchings on a finite time interval is established for perturbed systems. For general parameterized piecewise analytic systems, this is achieved locally by extending Sussmann's result; this result is applied to a class of nonlinear complementarity systems arising from contact mechanics and constrained dynamical optimization. Furthermore, the existence of a global uniform bound on the number of switchings is established for bimodal piecewise affine systems by exploiting affine structure, under mild conditions on system parameters. It is shown that this bound is independent of initial state perturbations.