Positivity and Stability of Continuous-Time Stochastic Linear Systems

This paper is concerned with the positivity and stability of linear systems in continuous-time form with stochastic disturbances. Firstly, the definition of stochastic positivity in the sense of probability is introduced, which characterizes the minimum level for a stochastic linear system to be positive. Secondly, through rigorous analysis, sufficient criterion is derived under which the stochastic differential equation is stochastically positive in the sense of probability. Next, by resorting to the properties of Metzler matrices, mathematical expectation of the solution for the stochastic linear system is investigated to be always positive under some mild restrictions. Then, the exponentially p-moment stability is addressed for the stochastic linear positive system. Finally, two numerical examples are provided to demonstrate the applicability and effectiveness of the derived theoretical results.

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