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Null-controllability of nonlinear infinite delay systems with restrained controls. (English) Zbl 0595.93007
For nonlinear infinite delay systems \[ \dot x(t)=L(t,x_ t)+B(t)u(t)+f(t,x(\cdot),u(\cdot))+\int^{0}_{- \infty}A(\theta)x(t\quad +\theta)d\theta, \] \[ x(t)=\psi (t),\quad t\in]-\infty,0] \] sufficient conditions for null-controllability are obtained. Here L(t,\(\psi)\) is continuous in t, linear in \(\psi\) and \(L(t,\psi)=\sum^{1}_{k=0}A_ k\psi (-t_ k)\), where B(t) is a continuous matrix function, A(\(\theta)\) is an \(n\times n\) matrix whose elements are Lebesgue integrable on \(]-\infty,0]\); \(f: I\times B\times L_ 2\to E^ n\) is a continuous function and the control \(u(t)\in \{u| u\in E^ m\), \(| u_ j| \leq 1\), \(j=1,...,m\}\) is a square-integrable function.
Reviewer: T.Tadumadze

MSC:
93B05 Controllability
34K35 Control problems for functional-differential equations
93C10 Nonlinear systems in control theory
93B03 Attainable sets, reachability
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93C99 Model systems in control theory
93D20 Asymptotic stability in control theory
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