Stabilization with a Specified External Gain for Linear MIMO Systems and Its Applications to Control of Networked Systems

TL;DR

This paper develops a method to stabilize linear MIMO systems with a specific external gain, enabling robust output synchronization in networked multi-agent systems through a novel normal form transformation and feedback design.

Contribution

It introduces a new approach using singular value decomposition to explicitly construct controllers that achieve stabilization with a specified external gain for MIMO systems.

Findings

Explicit controller construction for stabilization with external gain

Application to robust output synchronization in multi-agent systems

Effective handling of static and dynamic feedback scenarios

Abstract

This paper studies a stabilization problem for linear MIMO systems subject to external perturbation that further requires the closed-loop system render a specified gain from the external perturbation to the output. The problem arises from control of networked systems, in particular, robust output synchronization of heterogeneous linear MIMO multi-agent systems via output feedback/communication. We propose a new approach that converts a class of MIMO systems into a normal form via repeated singular value decomposition and prove that a stabilization controller with a specified external gain can be explicitly constructed for the normal form.Two scenarios with static state feedback and dynamic output feedback are investigated. By integrating the reference model and internal model techniques, the robust output synchronization problem for MIMO multi-agent systems is converted into a stabilization problem with a specified externalgain and solved by the developed approach.