Delay-dependent stability analysis of stochastic time-delay systems involving Poisson process

Abstract

The delay-dependent (D-D) stability problem is investigated for stochastic time-delay systems (STDSs) involving the Poisson process in this paper. Firstly, semi-martingale theory is conducted to tackle the jump information of Itô formula properly. Secondly, this paper studies the expectations of stochastic cross terms (SCTs) containing Poisson-type stochastic integrals (SIs), and proves that the expectation of the particular SCT is equal to the expectation of a Lebesgue integral. Thirdly, on the basis of the above results, this paper adopts the free weighting matrix (FWM) method to give a D-D stability condition by a linear matrix inequality (LMI). In the derivation, no bounding technique is used, and then the conservatism arising from the common bounding technique is avoided. Finally, an example is presented to show the effectiveness of the derived D-D stability condition.