Boundary PI controllers for a star-shaped network of 2 × 2 systems governed by hyperbolic partial differential equations

作     者：Trinh N.-T. Andrieu V. Xu C.-Z. 

作者机构：University of Lyon Laboratory LAGEP Bâtiment CPE University Lyon 1 France 

出 版 物：《IFAC-PapersOnLine》 

年 卷 期：2017年第50卷第1期

页      面：7070-7075页

主　　题：conservation laws Control of hyperbolic systems infinite-dimensional multi-agent systems Lyapunov methods networks output regulation for distributed parameter systems stability of distributed parameter systems 

摘      要：The paper is concerned with the PI control regulation of a star-shaped network of systems governed by hyperbolic partial differential equations. The control input and measured output are on the boundary. First, each system of the network is linearized and diagonalized with Riemann invariants. Then, by using Lyapunov direct method, the PI controller is proposed for a single system. Finally, we extend the PI control design for the star-shaped network of n subsystems. The exponential stability and output regulation of closed-loop systems are all proven with the aid of a strict Lyapunov functional. © 2017