Stability of systems with state-dependent and random delays

Abstract

The Lyapunov-Krasovskii theory is extended to systems with varying delay time. First we consider stochastic delay times, and derive sufficient conditions for stochastic global asymptotic stability. These conditions are of the 'standard' Riccati equation form, together with a bound on the expected rate of change of the time delay. Next we establish some results for the asymptotic stability of systems with state-dependent delay.