On Existence of Separable Contraction Metrics for Monotone Nonlinear Systems
For control theorists and engineers, this work provides theoretical foundations for scalable stability verification of large-scale nonlinear systems, though it is incremental as it builds on existing Lyapunov theory.
The paper proves conditions under which a contracting nonlinear system admits a separable contraction metric, enabling tractable stability analysis for large-scale networks. It extends results from positive linear systems to nonlinear systems and demonstrates applicability to distributed control design.
Finding separable certificates of stability is important for tractability of analysis methods for large-scale networked systems. In this paper we consider the question of when a nonlinear system which is contracting, i.e. all solutions are exponentially stable, can have that property verified by a separable metric. Making use of recent results in the theory of positive linear systems and separable Lyapunov functions, we prove several new results showing when this is possible, and discuss the application of to nonlinear distributed control design via convex optimization.