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arXiv · 1703.07071

On reduction of differential inclusions and Lyapunov stability

Rushikesh Kamalapurkar·Warren E. Dixon·Andrew R. Teel
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Abstract

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 point-wise 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.

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Rushikesh Kamalapurkar, Warren E. Dixon, Andrew R. Teel. 2017-03-21. On reduction of differential inclusions and Lyapunov stability. https://doi.org/10.1051/cocv%2F2019074

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