Delay-dependent stability and stabilisation of two-dimensional positive Markov jump systems with delays

This study considers the problem of exponential mean stability and stabilisation of two-dimensional positive Markov jump systems with delays. Necessary and sufficient delay-dependent conditions for exponential mean stability of the closed-loop system are first derived. Then, a design scheme based on a linear programming problem is proposed for obtaining parameters of a mode-dependent controller that makes the closed-loop system positive and exponentially mean stable. Finally, two numerical examples are presented to illustrate the effectiveness of the obtained results.