A Delay Margin Problem for the Stabilization of Stochastic Systems with Input Delay

Abstract

This paper is concerned with a delay margin problem for the stabilization of a discrete-time stochastic system with an input delay. First, it is shown that there always exists a margin M, such that this system is stabilizable for any delay $d\lt M$ and not stabilizable for any delay $d\geq M$. Secondly, the delay margin is presented by a quasi-convex LMIs optimization problem under some assumptions. Thirdly, analytical expressions of the delay margin are proposed in two special cases.