Distributed solving sylvester equations with an explicit exponential convergence

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.