Stabilization of Systems With Probabilistic Interval Input Delays and Its Applications to Networked Control Systems

Motivated by the study of a class of networked control systems, this correspondence paper is concerned with the design problem of stabilization controllers for linear systems with stochastic input delays. Different from the common assumptions on time delays, it is assumed here that the probability distribution of the delay taking values in some intervals is known a priori. By making full use of the information concerning the probability distribution of the delays, criteria for the stochastic stability and stabilization controller design are derived. Traditionally, in the case that the variation range of the time delay is available, the maximum allowable bound of time delays can be calculated to ensure the stability of the time-delay system. It is shown, via numerical examples, that such a maximum allowable bound could be made larger in the case that the probability distribution of the time delay is known.