Volume 26, 2020
|Number of page(s)||16|
|Published online||03 March 2020|
On reduction of differential inclusions and Lyapunov stability*
School of Mechanical and Aerospace Engineering, Oklahoma State University,
2 Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, USA.
3 Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA, USA.
** Corresponding author: firstname.lastname@example.org
Accepted: 25 November 2019
In this paper, locally Lipschitz, regular functions are utilized to identify and remove infeasible directions from set-valued maps that define differential inclusions. The resulting reduced set-valued map is pointwise smaller (in the sense of set containment) than the original set-valued map. The corresponding reduced differential inclusion, defined by the reduced set-valued map, is utilized to develop a generalized notion of a derivative for locally Lipschitz candidate Lyapunov functions in the direction(s) of a set-valued map. The developed generalized derivative yields less conservative statements of Lyapunov stability theorems, invariance theorems, invariance-like results, and Matrosov theorems for differential inclusions. Included illustrative examples demonstrate the utility of the developed theory.
Mathematics Subject Classification: 93D02
Key words: Differential inclusions / stability / hybrid systems / nonlinear systems
This research is supported in part by NSF award numbers 1509516 and 1508757, ONR award number N00014-13-1-0151, AFRL award number FA8651-19-2-0009, and AFOSR award number FA9550-15-1-0155. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the sponsoring agency.
© EDP Sciences, SMAI 2020
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