Stability and stabilization of discrete-time linear stochastic positive system

Abstract

Positive systems are one class of systems with special properties that are prevalent in both macroscopic and microscopic domains. Stochastic positive systems have important theoretical value and wide application value in biology, economics and other fields. Therefore, the research on stochastic positive systems is of great significance. The paper investigates the stability with probability 1(w.p.1.) and stabilization designs of the discrete linear stochastic positive systems. Firstly, based on the comparison principle, the conditions for discrete linear stochastic positive systems with state probability constraints to be the stability with probability one is proposed. Secondly, based on this, the problem of stabilization for discrete linear stochastic controlled positive system is considered. Some sufficient conditions are proposed for constructing stable w.p.1 feedback controller. Finally, we verified the validity of the conclusions with numerical arithmetic examples based on linear programming theory.