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Control of nonlinear variable structure systems. (English) Zbl 0622.93026
This paper is devoted to the research of different nonlinear control problems with variable structure described by $$\dot x=f(t,x,u)$$, $$x(t)\in R^ n$$, $$u(t)\subset V\in R^ m$$ with sliding manifold $$S(x)=0,S(x)\in R^ m$$. Controllability conditions based on Filipov’s definition of the solution of ordinary differential equations with discontinuous right-hand sides are derived. The derived conditions are illustrated via particular control problems with variable structure.