Distributed solving Sylvester equations with fractional order dynamics

This paper addresses distributed computation Sylvester equations of the form $${A}{X}+{X}{B}={C}$$ with fractional order dynamics. By partitioning parameter matrices A, B and C, we transfer the problem of distributed solving Sylvester equations as two distributed optimization models and design two fractional order continuous-time algorithms, which have more design freedom and have potential to obtain better convergence performance than that of existing first order algorithms. Then, rewriting distributed algorithms as corresponding frequency distributed models, we design Lyapunov functions and prove that proposed algorithms asymptotically converge to an exact or least squares solution. Finally, we validate the effectiveness of proposed algorithms by providing a numerical example