Null controllability of nonlinear infinite delay systems with time varying multiple delays in control
Nonlinear time-varying control systems with time-varying infinite multiple delays in the control are considered. Using Schauder's fixed point theorem for nonlinear mappings in Banach spaces, a sufficient condition for relative null-controllability in a given time interval is formulated and proved. More precisely, it is shown that if the uncontrolled dynamical system is uniformly asymptotically stable, and if the linear nonperturbed system is relative null-controllable, then the nonlinear infinite delay system is relative null-controllable. Moreover, some remarks and comments on relative controllability for dynamical systems with delays in the control are given. Thus, theorems presented by the reviewer [\textit{J. Klamka}, Int. J. Control 24, 869-878 (1976; Zbl 0342.93006)], where systems with multiple finite delays in the control were considered, are extended here to infinite delay controllability.
scientific article; zbMATH DE number 915106
scientific article