On controllability and null controllability of linear systems with distributed delays in the control (Q1177309)

Linear, finite-dimensional, time-varying dynamical systems with distributed delays in the control are considered. Using the results on relative controllability given in the paper of \textit{J. Klamka} [IEEE Trans. Automatic Control AC-21, 594-595 (1976; Zbl 0332.93013)], and conditions for asymptotic stability, sufficient conditions for relative controllability with constraints on the controls are formulated and proved. Sufficient condition for null relative controllability with constraints on the controls are also derived. Finally, as a special case, sufficient conditions for relative and null relative controllability with constraints for dynamical systems with multiple lumped delays in the control are presented. A simple, illustrative numerical example is given. Similar controllability problems for nonlinear dynamical systems with distributed delays in the control have been considered in \textit{J. Klamka}, Int. J. Control Vol. 28, 307-312 (1978; Zbl 0402.93012).