Decentralized H2 Control for Discrete-Time Networked Systems With Positivity Constraint

In this brief, we study the decentralized $H_{2}$ state-feedback control problem for networked discrete-time systems with positivity constraint. This problem (for a single positive system), raised recently in the area of positive systems theory, is known to be challenging due to its inherent nonconvexity. In contrast to most works, which only provide sufficient synthesis conditions for a single positive system, we study this problem within a primal-dual scheme, in which necessary and sufficient synthesis conditions are proposed for networked positive systems. Based on the equivalent conditions, we develop a primal-dual iterative algorithm for solution, which helps prevent from converging to a local minimum. In the simulation, two illustrative examples are employed for verification of our proposed results.

Automated summary

In this paper, we study the decentralized H2 state-feedback control problem for networked discrete-time systems with positivity constraint. We propose necessary and sufficient synthesis conditions for networked positive systems, unlike most previous works that only provide sufficient conditions for a single positive system. We develop a primal-dual iterative algorithm based on these conditions to solve the problem and avoid converging to a local minimum. Two illustrative examples are used to verify our proposed results.