Relative controllability of nonlinear delayed multi-agent systems

Abstract

Controllability of nonlinear delayed leader-follower multi-agent system with fixed communication topology is introduced. A solution of a semilinear time-delay control system and Gramian matrix for the linear part which has Kronecker delay perturbation of exponential matrix function are given. The assumptions and conditions under which the nonlinear delay multi-agent system can be controlled are determined thanks to control problem into fixed point problem. A comprehensive example to illustrate given theoretical contents is presented.