Output Synchronization of Heterogeneous Networked Linear MIMO Systems: $\gamma$-Stabilization and $H_\infty$ Control

Abstract

This article studies robust output synchronization of heterogeneous linear multiple-input multipleoutput (MIMO) multiagent systems via output communication/feedback. The problem can be technically converted into two coupled problems, namely, a well-solved perturbed consensus problem and perturbed regulation of each individual agent. The latter motivates the so-called γ-stabilization problem, which requires the closed-loop system render a particular input-to-output gain, viewing from external perturbation to output to be less than a specified value. It is shown that an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller solves the y-stabilization problem and thus is sufficient for the robust output synchronization problem. Nevertheless, when an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller does not exist, a new approach is proposed to convert a particular class of MIMO systems into a normal form via repeated singular value decomposition, for which a stabilization controller can be explicitly constructed. By integrating the reference model and internal model techniques, the robust output synchronization problem is solved by the developed approach.