Paper Info
Title
A multiple-comparison-systems method for distributed stability analysis of large-scale nonlinear systems.
Abstract
Lyapunov functions provide a tool to analyze the stability of nonlinear systems without extensively solving the dynamics. Recent advances in sum-of-squares methods have enabled the algorithmic computation of Lyapunov functions for polynomial systems. However, for general large-scale nonlinear networks it is yet very difficult, and often impossible, both computationally and analytically, to find Lyapunov functions. In such cases, a system decomposition coupled to a vector Lyapunov functions approach provides a feasible alternative by analyzing the stability of the nonlinear network through a reduced-order comparison system. However, finding such a comparison system is not trivial and often, for a nonlinear network, there does not exist a single comparison system. In this work, we propose a multiple comparison systems approach for the algorithmic stability analysis of nonlinear systems. Using sum-of-squares methods we design a scalable and distributed algorithm which enables the computation of comparison systems using only communications between the neighboring subsystems. We demonstrate the algorithm by applying it to an arbitrarily generated network of interacting Van der Pol oscillators.
Year
DOI
Venue
2017
10.1016/j.automatica.2016.12.003
Automatica
Keywords
Field
DocType
Lyapunov stability,Dynamical systems,Sum-of-squares optimization,Disturbance analysis,Interconnected systems
Lyapunov function,Mathematical optimization,Nonlinear system,Stability (learning theory),Control theory,Lyapunov stability,Lyapunov optimization,Lyapunov redesign,Distributed algorithm,Dynamical systems theory,Mathematics
Journal
Volume
Issue
ISSN
78
1
0005-1098
Citations 
PageRank 
References 
2
0.38
9
Authors
2
Name
Order
Citations
PageRank
Soumya Kundu185.87
Marian Anghel2699.68