Time-invariant Linear Systems with Delay

Abstract

This chapter is devoted to time-invariant (autonomous) linear systems with delay. In the terms of the characteristic matrix-valued function we derive estimates for the $L^p$- and C-norms of fundamental solutions. By these estimates below we obtain stability conditions for linear time-variant and nonlinear systems. Moreover, these estimates enable us to establish bounds for the region of attraction of the stationary solutions of nonlinear systems.