Abstract

The central aim of this talk is to explain why any jointly controllable, jointly observable multi-channel linear system with a strongly connected neighbor {communication} graph can be exponentially stabilized with arbitrarily fast convergence using a time-invariant  distributed linear control. This result can be established using a distributed observer-based control architecture analogous to the familiar centralized observer-based  architecture used to control a controllable, observable, linear system. A key consequence of this finding is that the well-known fixed spectrum {set of fixed modes} of a multi-channel linear system is no longer an obstacle to the system's regulation provided distributed rather than decentralized control is used. It will also be explained how to avoid this obstacle using distributed control without restricting the control architecture to be of the  observer-based type. Using these ideas, a solution will also be given to the distributed set-point control problem for a multi-channel linear system in which each and every agent with access to the system is able to independently adjust its controlled output to any desired set-point value. Often overlooked in the study of distributed control are the effects of communication network transmission delays. It will be explained why in the face of such delays, exponential stabilization at a prescribed convergence rate can still be achieved with distributed control, at least for discrete-time, multi-channel linear systems.