Stabilization of Positive Markovian Jump Systems with Input Saturation: A Linear Programming Approach

This paper proposes a linear programming (LP) approach for stabilization of positive Markovian jump systems (PMJSs) with input saturation. First of all, we derive the sufficient conditions for stabilization of PMJSs with input saturation based on the linear co-positive Lyapunov function. However, since the decision variables in the obtained conditions are mutually coupled, the conditions are not linear. Therefore, to obtain the condition that can be solved by the LP, we propose the methods to properly choose the decision variables. Furthermore, we give a process to acquire the largest domain of attraction. Finally, we suggest two numerical examples to illustrate the validity of the proposed methods.