Smoothness of solutions to the damping problem for nonstationary control system with delay of neutral type on the whole interval. (English. Russian original) Zbl 07891524
J. Math. Sci., New York 283, No. 2, 167-182 (2024); translation from Sovrem. Mat., Fundam. Napravl. 69, No. 1, 1-17 (2023).
Summary: We consider the damping problem for a nonstationary control system described by a system of differential-difference equations of neutral type with smooth matrix coefficients and several delays. This problem is equivalent to the boundary-value problem for a system of second-order differential-difference equations, which has a unique generalized solution. It is proved that the smoothness of this solution can be violated on the considered interval and is preserved only on some subintervals. Sufficient conditions for the initial function are obtained to ensure the smoothness of the generalized solution over the entire interval.
MSC:
| 34K35 | Control problems for functional-differential equations |
| 34K40 | Neutral functional-differential equations |
| 34K10 | Boundary value problems for functional-differential equations |
| 34K06 | Linear functional-differential equations |
| 93C05 | Linear systems in control theory |
| 93C23 | Control/observation systems governed by functional-differential equations |
Keywords:
neutral-type differential-difference equation; damping problem for control system with aftereffect; Krasovskii problem; generalized solution; smoothness of solutionReferences:
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