On the Lipschitz behavior of solution maps of a class of differential inclusions. (English) Zbl 1325.34024

Adam, Lukáš

Set-Valued Var. Anal. 23, No. 3, 559-575 (2015).

Summary: We consider a general differential inclusion which is parameterized by a parameter. We perform time discretization and present conditions under which the discretized solution map is locally Lipschitz. Further, if the Lipschitzian modulus is bounded in some sense, we show that it is possible to obtain the local Lipschitzian property even for the original (not discretized) solution map. We conclude the paper with an example concerning stability analysis of nonregular electrical circuits with ideal diodes.

MSC:

34A60	Ordinary differential inclusions
34H05	Control problems involving ordinary differential equations
49K21	Optimality conditions for problems involving relations other than differential equations
34A36	Discontinuous ordinary differential equations

Keywords:

differential inclusions; Lipschitzian continuity; stability; variational analysis; electrical circuits

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