Distributed Feedback Control of Multi-Channel Linear Systems

Fengjiao Liu, Lili Wang, Daniel Fullmer, A. Stephen Morse

This paper establishes that any jointly controllable and jointly observable multi-channel linear system with a strongly connected neighbor (communication) graph can be exponentially stabilized with an arbitrarily fast convergence rate using a time-invariant distributed linear control. A key step towards this end is showing that the fixed spectrum (i.e., the set of fixed modes) of a multi-channel linear system will no longer be an obstacle to the effective control of such a system provided that distributed rather than classical decentralized control is used. This is true for both continuous-time and discrete-time systems. Using these ideas, a solution is 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 transmission delays across the network. It is explained why in the face of such delays, exponential stabilization at any prescribed convergence rate can still be achieved with distributed control, at least for discrete-time multi-channel linear systems.

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