Positive Decentralized Stabilization of Large-Scale Interconnected Dynamic Systems

Bahram Shafai, Fatemeh Zarei, Mehrdad Saif

Abstract: This paper considers the problem of decentralized positive stabilization of large-scale interconnected dynamic systems. The main challenge is how to design a state feedback controller for each subsystem locally so that the stability and positivity of the overall interconnected system can be guaranteed. We assume that subsystems are positive and unstable. However, the positive stabilization can be employed for general unstable interconnected subsystems as well. Two approaches are outlined to formulate and solve the problem using LMI. The first approach is derived based on positive stabilization of local subsystems while the second approach considers the global positive stabilization. Finally, both approaches are tied to an elegant sequential procedure using Schur complement of block diagonal Metzler matrices. The procedure is outlined in details and numerical examples are included to support the theoretical results.