Exponential mean stability of stochastic discrete-time systems with time-varying delays via an IPR-based approach
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.