Stabilization of a class of distributional convolution equations. (English) Zbl 0566.93048

Noldus, E.

Int. J. Control 41, 947-960 (1985).

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

Keywords:

functional-differential systems; linear state feedback

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