比较原理与随机时滞系统的稳定性

COMPARISON PRINCIPLE AND THE STABILITY OF TIME-DELAY STOCHASTIC SYSTEMS

建立了具有随机时变滞后的线性随机系统的比较原理，并用比较原理给出了随机滞后系统P阶均值各种稳定性的判别准则．

Consider the n-dimensional linear stochastic delay--differential system x(t, w) = A(t, w)x(t, w) +B(t, w)x(t-y(t, w), w), where the n2 elements of A, n2 elements of B, and the delay y are combined to a vector ξ It is assumed that the process {ξ(t, w): t ≥to} is an almostsurely bounded right-continuous strong Markov process. By employing vector Lyapunov-like functions and the theory of systems of delay-differential inequalities, a very general comparison theorem for the above system is developed. Furthermore, sufficient conditions are given for the stability of solutions in the p-order mean.