On observability of systems of linear functional-differential equations (Q1357953)

The observability problem for linear continuous-time functional-differential dynamical systems is considered. Using methods taken from functional analysis, necessary and sufficient conditions for observability in finite time for general linear systems are formulated and proved. The general theory is then applied to derive necessary and sufficient conditions for observability in finite time of linear functional-differential dynamical systems represented by differential equations with one constant delay in the state variables. Two simple illustrative examples are given. Moreover, some remarks and comments on observability problems for linear dynamical systems are presented. Similar observability problems for delayed dynamical systems are considered in the paper [\textit{B. Sh. Shklyar}, Sov. Phys., Dokl. 24, 711-713 (1979); translation from Dokl. Akad. Nauk SSSR 248, 549-552 (1979; Zbl 0434.93012)].