STABILITY ANALYSIS OF LINEAR DELAY-DIFFERENTIAL SYSTEMS

In this paper, a necessary and sufficient condition of asymptotic stability independent of delay (AS i.o.d.) of a class of composite retarded systems is presented. A corollary of this condition shows that the condition a(ii) < 0 is also necessary for AS i.o.d. of the system (*) x(i) = SIGMA(j = 1)n [a(ij)x(j) + b(ij)x(j)(t - tau)] with the quasidominant negative diagonal of matrix [(-1)delta(ij)\a(ij)\ + \b(ij)\]. Next, a new sufficient condition for AS i.o.d. of the retarded system is given by the spectral radius of a nonnegative matrix. In this condition, the coefficient matrix A = (a(ij)) is not required to be diagonalizable or the measure mu(A) < 0 for the system (*). Furthermore, a stability criterion for a class of neutral systems is also given in terms of a complex matrix equation. These results are compared with other previous results by several examples.