Stabilization of a class of distributional convolution equations. (English) Zbl 0566.93048
The paper deals with the stabilization of the system
\[
(1)\quad \dot x(t)=A_ 0x(t)+A_ 1x(t-h)+\int^{h}_{0}A(s)x(t-s)ds+B_ 0u(t)
\]
by using the linear state feedback \(u(t)=-Kx(t)\). It is shown, in particular, that if \((A_ 0,B_ 0)\) is controllable then the system (1) is stabilizable if \(\| A_ 1\|\) and \(\| A(s)\|\), \(0\leq s\leq h\), are sufficiently small. An illustrative example is also given.
Reviewer: V.Marchenko
MSC:
| 93D15 | Stabilization of systems by feedback |
| 34K35 | Control problems for functional-differential equations |
| 93C05 | Linear systems in control theory |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 46F10 | Operations with distributions and generalized functions |
| 42A85 | Convolution, factorization for one variable harmonic analysis |
| 34K20 | Stability theory of functional-differential equations |
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