TY - JOUR
T1 - Decentralized control of interconnected positive systems using L 1-induced norm characterization
AU - Ebihara, Yoshio
AU - Peaucelle, Dimitri
AU - Arzelier, Denis
PY - 2012
Y1 - 2012
N2 - This study concerns decentralized control of interconnected positive systems. The main issue is how to design a controller for each subsystem locally so that positivity and stability of the overall interconnected system can be attained. Under a specific interconnection structure, we will show that such a controller can be designed optimally without any information about the rest of the positive subsystems. This achievement is based on our recent characterization of stability of interconnected positive systems in terms of the L1-induced norm of each subsystem, where the L1-induced norm is evaluated with positive weighting vectors that are coupled mutually over the subsystems. The key observation in this study is that, under the specific interconnection structure, we can decouple the L1-induced norm conditions completely. We thus reduce the original stabilization problem into a set of L1-induced norm optimal controller synthesis problems each of which can be solved indeed locally. In particular, the L1-induced norm optimal controller synthesis can be done efficiently by solving a semidefinite programming problem.
AB - This study concerns decentralized control of interconnected positive systems. The main issue is how to design a controller for each subsystem locally so that positivity and stability of the overall interconnected system can be attained. Under a specific interconnection structure, we will show that such a controller can be designed optimally without any information about the rest of the positive subsystems. This achievement is based on our recent characterization of stability of interconnected positive systems in terms of the L1-induced norm of each subsystem, where the L1-induced norm is evaluated with positive weighting vectors that are coupled mutually over the subsystems. The key observation in this study is that, under the specific interconnection structure, we can decouple the L1-induced norm conditions completely. We thus reduce the original stabilization problem into a set of L1-induced norm optimal controller synthesis problems each of which can be solved indeed locally. In particular, the L1-induced norm optimal controller synthesis can be done efficiently by solving a semidefinite programming problem.
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U2 - 10.1109/CDC.2012.6427022
DO - 10.1109/CDC.2012.6427022
M3 - Conference article
AN - SCOPUS:84874272037
SP - 6653
EP - 6658
JO - Proceedings of the IEEE Conference on Decision and Control
JF - Proceedings of the IEEE Conference on Decision and Control
SN - 0191-2216
M1 - 6427022
T2 - 51st IEEE Conference on Decision and Control, CDC 2012
Y2 - 10 December 2012 through 13 December 2012
ER -