Complete calming and stabilization of linear autonomous systems with delay

Abstract

The problems of complete controllability and stabilizability for linear autonomous systems of delayed and neutral type are considered. For a second-order system with one input, it is supposed that the complete controllability criterion holds, and a controller with concentrated delay is constructed in such a way that the closed-loop system turns out to be pointwise degenerate, and thus provide complete original system calming down (complete calming controller). When the complete calming controller with distributed delay is being chosen, the stabilization problem is being simultaneously solved.