Stability of some systems with distributed delay

Asymptotic stability of linear equations with distributed delay is investigated. Both independent-of-delay (i.o.d.) and delay-dependent (d.d.) stability conditions are formulated in terms of existence of positive definite solutions to Riccati matrix equations. The approach of deriving various Riccati equations using the direct Liapunov-Krassovskii method is proposed. The results, that are presented here in the single-delay case, can easily be enlarged to multiple delays.