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Boundary value problems and control problems for linear difference systems with aftereffect. (English. Russian original) Zbl 0836.34087
Russ. Math. 37, No. 5, 1-12 (1993); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1993, No. 5 (372), 3-16 (1993).
The author’s intension is to present discrete analogs of certain results from the theory of boundary value problems for functional-differential equations and control systems with delays. First he considers linear systems $${\mathcal L} x = f$$ with $$({\mathcal L} x) (t) = x(t + 1) - \sum^t_{i = 0} A(t,i) x(i)$$ as well as quasilinear systems $${\mathcal L} x = Fx$$ where $$F$$ is some nonlinear operator, together with boundary conditions $$lx = \alpha$$ where $$l$$ is a linear vector functional, and obtains sufficient conditions for existence of a solution. After that he considers nonlinear control systems of the type $${\mathcal L} x = Gu + F(x,u)$$ and presents sufficient conditions for complete controllability.
Reviewer: W.Müller (Berlin)

##### MSC:
 34K35 Control problems for functional-differential equations 93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) 39A10 Additive difference equations 34K10 Boundary value problems for functional-differential equations