Ổn định trung bình mũ của hệ ngẫu nhiên rời rạc có độ trễ biến thiên theo thời gian, thông qua cách tiếp cận dựa trên IPR

Abstract

The internally positive representation (IPR) technique helps to reformulate the stability problem of nonpositive linear systems into the stability problem of a class of positive linear systems, whose matrices are constructed from the extraction of matrices of the considered system. In this paper, we present a development of the IPR-based approach to a class of stochastic discrete-time systems with time-delays. Our study is devoted to the problem of finding an α-exponential estimate of the absolute of the expectation of the state vector. For this, firstly, we investigate the the exponential stability problem for a class of positive stochastic discrete-time systems with time-varying delays. Here, both the positivity and the exponential stability are considered in the sense of expectation. Next, by using the IPR technique, we develop the obtained result to a class of non-positive stochastic systems. Finally, a numerical example is given to illustrate the effectiveness of the developed approach.