Abstract

In this article, the stochastic positivity and stability problems are addressed for the linear systems in discrete-time form. Firstly, a new and novel definition is given to describe the positivity characteristic of certain systems in the sense of probability. Then, by rigorous discussion/analysis, sufficient criteria are established, which guarantee that the linear system is stochastically positive in the sense of probability with respect to some given threshold. After that, certain nonnegativeness property is provided for the mathematical expectation of the solutions concerning the considered stochastic linear system. Subsequently, stochastic stability in different forms is studied. Finally, illustrative examples are provided to demonstrate the validity/effectiveness of the developed results.

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