Distributed Solver for Discrete-Time Lyapunov Equations Over Dynamic Networks with Linear Convergence Rate

This paper investigates the problem of solving discrete-time Lyapunov equations (DTLE) over a multi-agent system, where every agent has access to its local information and communicates with its neighbors. To obtain a solution to DTLE, a distributed algorithm with uncoordinated constant step sizes is proposed over time-varying topologies. The convergence properties and the range of constant step sizes of the proposed algorithm are analyzed. Moreover, a linear convergence rate is proved and the convergence performances over dynamic networks are verified by numerical simulations.