Exponential stabilization of Functional Differential Equations

Abstract

Let us consider the autonomous functional differential equation

$$ \dot{x} = \int\limits_{{ - h}}^{0} {dN(z)x(t + z)\quad t \geqslant 0} $$

((1))

where: z →N(z) is an nxn matrix of bounded variation on the interval [-h,0], t →x(t) is a continuous vector function for t≥-h.