Robust stability and performance analysis of positive systems using linear programming

This work presents a new necessary and sufficient condition for robust stability and robust performance of positive linear time invariant (LTI) systems with structured uncertainties. It is known that robustness analysis of LTI systems with structured uncertainties requires evaluation of structured singular value (SSV), which is known to be NP-hard. This paper shows that for positive systems, the structured singular value can be estimated efficiently using linear programming. Thus, the robustness analysis of positive systems is simplified to easily verifiable conditions that scale linearly with the dimensions of the system. This property finds great utility in analysis and synthesis of large scale positive systems with distributed control strategies.