This paper studies the stochastic stability of positive Markov jump linear systems with a fixed dwell time. By constructing an auxiliary system that originated from the initial system with state jumps, sufficient and necessary conditions of stochastic stability for positive Markov jump linear systems are obtained with both exactly known and partially known transition rates. The main idea in the latter case is applying a convex combination to convert bilinear programming into linear programming problems. On this basis, multiple piecewise linear co-positive Lyapunov functions are provided to achieve less conservative results. Then state feedback controller is designed to stabilize the positive Markov jump linear systems by solving linear programming problems. Numerical examples are presented to illustrate the viability of our conclusions.

本文研究了具有固定停留时间的正Markov跳跃线性系统的随机稳定性。通过构造一个源于具有状态跃迁的初始系统的辅助系统，可以以已知的和部分已知的跃迁速率获得正马尔可夫跃迁线性系统的随机稳定性的充分和必要条件。在后一种情况下的主要思想是应用凸组合将双线性规划转换为线性规划问题。在此基础上，提供了多个分段线性共正Lyapunov函数，以实现较少的保守结果。然后设计状态反馈控制器，通过解决线性规划问题来稳定正Markov跳跃线性系统。数值例子说明了我们结论的可行性。