Positivity-based control system synthesis using alternating LMIs

This paper describes a method to synthesize positivity-based controllers for flexible systems. A strictly positive real controller guarantees unconditional stability in the closed-loop system with respect to plant parametric uncertainty provided the plant is positive real. By adopting static output feedbacks and the performance specification in terms of decay rate, the positivity approach results in a simple setting involving coupled LMIs. The alternating LMIs method is proposed in this paper to solve the synthesis problem. The Draper's tetrahedral truss example is used to demonstrate the effectiveness of this method in solving flexible structure robust control problems.