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Conditions for the continuous establishment, from results of observation, of the current state of a linear system with time-lag. (English. Russian original) Zbl 0622.34083

Differ. Equations 23, No. 2, 153-161 (1987); translation from Differ. Uravn. 23, No. 2, 217-227 (1987).
Consider the system (*) \(\dot x(t)=A_ 0x(t)+A_ 1x(t-1)\), \(y(t)=G_ 0x(t)+G_ 1x(t-1),\) \(t>0\); \(x(t)=x_ 0(t)\), -1\(\leq t\leq 0\), where \(x(t)\in {\mathbb{R}}^ n\), \(y(t)\in {\mathbb{R}}^ m\) and the initial function \(x_ 0(.): [-1,0]\to {\mathbb{R}}^ n\) is continuous. Define the reconstruction operator \(R_ T: Y_ T\to C([-1,0],{\mathbb{R}}^ n)\) by \(R_ Ty=x_ T\), \(x_ t=\{x(t+s): -1\leq s\leq 0\}\), where \(Y_ T\) is the set of attainable outputs on [0,T]. The author shows that if (*) is spectrally observable then \(R_ T\) is continuous for T sufficiently large.
Reviewer: M.M.Konstantinov

MSC:

34K35 Control problems for functional-differential equations
34H05 Control problems involving ordinary differential equations
93B07 Observability
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