Application of asymptotic estimates to the study of controllability of linear time-invariant systems of delay type (Q1897954)

Linear time-invariant control systems with lumped incommensurable delays and distributed delays both in the state and control variables are considered. It is shown, that spectral controllability of the delayed system is a sufficient condition for the null controllability. The proof of this result is based on asymptotic expansions for large zeros of entire functions from a certain class. Moreover, the paper contains several remarks and comments concerning the properties of the entire functions and zeros of entire functions. Similar spectral controllability and null controllability problems were studied in the papers [\textit{A. W. Olbrot} and \textit{L. Pandolfi}, Int. J. Control 47, No. 1, 193-208 (1988; Zbl 0662.93008)], and [\textit{M. W. Spong} and \textit{T. J. Tarn}, IEEE Trans. Autom. Control AC-26, No. 2, 527-528 (1981; Zbl 0474.93014)], but in rather less general setting.