${\mathcal K}$-monotonicity and feedback synthesis for incrementally stable networks

TL;DR

This paper explores how monotonicity properties in networked nonlinear systems facilitate modular control design, enabling scalable stabilization through linear programming by embedding variational systems into positive systems.

Contribution

It introduces a novel approach to network stabilization by leveraging monotonicity and exponential dissipativity, leading to a modular design algorithm based on linear programming.

Findings

Variational systems of monotone systems can be embedded into positive systems.

Enforcing monotonicity and dissipativity enables modular stabilization.

The proposed method simplifies control design via linear programming.

Abstract

We discuss the role of monotonicity in enabling numerically tractable modular control design for networked nonlinear systems. We first show that the variational systems of monotone systems can be embedded into positive systems. Utilizing this embedding, we show how to solve a network stabilization problem by enforcing monotonicity and exponential dissipativity of the network sub-components. Such modular approach leads to a design algorithm based on a sequence of linear programming problems.