Distributed Solving Sylvester equations with an explicit exponential Convergence. Issue 2 (2020)

• Record Type: Journal Article
• Authors: Cheng, Songsong; Zeng, Xianlin; Hong, Yiguang
• Is Part Of: IFAC-PapersOnLine. Volume 53:Issue 2(2020)
• Page Start: 3260
• Page End: 3265
• Publication Date: 2020
• Subjects: Sylvester equations -- Distributed optimization -- Least squares solution -- exponential convergence; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2020.12.1129
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: This paper addresses distributed achieving the least squares solution of Sylvester equations in the form of AX + XB = C. By decomposing the parameter matrices A, B and C, we formulate the problem of distributed solving Sylvester equations as a distributed optimization model and propose a continuous-time algorithm from the primal-dual viewpoint. Then, by constructing a Lyapunov function, we prove that the proposed algorithm can achieve a least squares solution of Sylvester equations with an explicit exponential convergence rate. Additionally, we illustrate the convergence performance by using a numerical example.