Synchronization of Identical Boundary-Actuated Semilinear Infinite-Dimensional Systems

TL;DR

This paper develops conditions for achieving synchronization in boundary-actuated semilinear infinite-dimensional systems, including hyperbolic conservation laws, using matrix inequalities for control design.

Contribution

It introduces new synchronization conditions for boundary-controlled infinite-dimensional systems and provides matrix inequality-based design methods for hyperbolic systems.

Findings

Sufficient conditions for asymptotic synchronization are established.

Conditions can be expressed as linear matrix inequalities for certain systems.

The approach applies to hyperbolic semilinear conservation laws.

Abstract

This paper deals with synchronization of a class of infinite-dimensional systems. The considered network is described by a collection of semilinear Lipschitz boundary-actuated infinite-dimensional dynamics. For undirected connected graphs, sufficient conditions for asymptotic synchronization are established. We show that the proposed conditions when applied to systems of hyperbolic semilinear conservation laws can be recast into a set of matrix inequalities. For this class of systems, sufficient conditions in the form of linear matrix inequalities for the design of synchronizing policies are provided.