A problem of modal control in a linear neutral system. (English) Zbl 1003.34070
The following problem is considered: find the vectors \(c_k\in \mathbb{R}^n\), \(k= 0,\dots, m\), such that the characteristic quasi-polynomial of the closed system
\[
{d\over dt} [x(t)- Dx(t-\tau)]= Ax(t)+ A_1 x(t-\tau)+ bu(t),
\]
\[ u(t)= \sum^m_{k= 0} c_k x(t- k\tau),\quad t\geq 0,\quad \tau> 0, \] has coefficients given in advance. The problem is solved for canonical neutral systems.
\[ u(t)= \sum^m_{k= 0} c_k x(t- k\tau),\quad t\geq 0,\quad \tau> 0, \] has coefficients given in advance. The problem is solved for canonical neutral systems.
Reviewer: T.Tadumadze (Tbilisi)
MSC:
34K35 | Control problems for functional-differential equations |
49K25 | Optimal control problems with equations with ret.arguments (nec.) (MSC2000) |
34K40 | Neutral functional-differential equations |