Boundary value problems and control problems for linear difference systems with aftereffect. (English. Russian original) Zbl 0836.34087

Andrianov, D. L.

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

Keywords:

boundary value problems; existence; complete controllability