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On singular passages to the limit in case of extension of discontinuous systems. (Russian) Zbl 0654.34055
An augmentation averaging scheme is proposed for predetermination of the sliding system $$\dot s=f(s,x,u(s))$$, $$\dot x=F(s,x,u(s))$$, where $$s(t)\in {\mathbb{R}}^ 1$$, $$x(t)\in {\mathbb{R}}^ n$$ and $$u(s)=sign(s)$$.
Reviewer: D.Baniov

##### MSC:
 34H05 Control problems involving ordinary differential equations
##### Keywords:
averaging scheme; sliding system