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Monotonicity Along Solutions to Constrained Differential Inclusions


In this paper, a general framework is proposed to determine when a scalar function is nonincreasing along solutions to differential inclusions defined on constrained sets. To the best of our knowledge, this problem has not been yet treated in the literature, and is important, for example, for the analysis of hybrid systems modeled by hybrid inclusions. The proposed characterizations are infinitesimal and do not require any knowledge about the system's solutions. Furthermore, the problem is addressed under different regularity properties of the considered scalar function, including the case of lower semi-continuous functions, the case of locally Lipschitz and regular functions, and finally the case of continuously differentiable functions.

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