Vodichev, A. V. 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 Cited in 2 Documents MSC: 34K35 Control problems for functional-differential equations 34H05 Control problems involving ordinary differential equations 93B07 Observability Keywords:characteristic matrix; characteristic quasipolynomial equation; first order differential equation PDFBibTeX XMLCite \textit{A. V. Vodichev}, Differ. Equations 23, No. 2, 153--161 (1987; Zbl 0622.34083); translation from Differ. Uravn. 23, No. 2, 217--227 (1987)