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

TL;DR

This paper presents a distributed algorithm for solving discrete-time Lyapunov equations over dynamic networks, achieving linear convergence with uncoordinated step sizes, validated through theoretical analysis and simulations.

Contribution

It introduces a novel distributed solver for DTLE with proven linear convergence over time-varying networks, accommodating uncoordinated step sizes.

Findings

The algorithm converges linearly under certain conditions.

Convergence is maintained over dynamic network topologies.

Numerical simulations confirm theoretical results.

Abstract

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.