A frequency domain method for stochastic time delay

Random time delay problem is a key problem in networked control systems (NCSs) and uncertain metrology delay systems. Different from the ordinary delay, the random delay is usually described in time domain. In this paper, a Laplace transform strategy is used to analyze random time delay problem. Firstly, the various Laplace transforms of random variables are discussed; then, based on the output response expectation equivalent principle, the appropriate Laplace transform for random delay is chosen. To use the Laplace transform, the random time delay can be discussed in frequency domain. In particular, some difficult random delay problem in the time domain can be very simple to solve in the frequency domain. Finally, simulations are given to verify the proposed strategy of this paper and some interesting results has been obtained.