TY - JOUR

T1 - The state feedback regulator problem for regular linear systems

AU - Natarajan, Vivek

AU - Gilliam, David S.

AU - Weiss, George

N1 - Publisher Copyright:
© 2014 IEEE.

PY - 2014/10/1

Y1 - 2014/10/1

N2 - This paper is about the state feedback regulator problem for infinite-dimensional linear systems. The plant, assumed to be an exponentially stable regular linear system, is driven by a linear (possibly infinite-dimensional) exosystem via a disturbance signal. The exosystem has its spectrum in the closed right half-plane and also generates the reference signal for the plant output. The regulator problem is to design a controller that, while guaranteeing the stability of the closed-loop system without the exosystem, drives the tracking error to zero. A particular version of this problem is the state feedback regulator problem in which the states of the exosystem and the plant are known to the controller. Under suitable assumptions, we show that the latter problem is solvable if and only if a pair of algebraic equations, called the regulator equations, is solvable. We derive conditions, in terms of the transfer function of the plant and eigenvalues of the exosystem, for the solvability of the regulator equations. Three examples illustrating the theory are presented.

AB - This paper is about the state feedback regulator problem for infinite-dimensional linear systems. The plant, assumed to be an exponentially stable regular linear system, is driven by a linear (possibly infinite-dimensional) exosystem via a disturbance signal. The exosystem has its spectrum in the closed right half-plane and also generates the reference signal for the plant output. The regulator problem is to design a controller that, while guaranteeing the stability of the closed-loop system without the exosystem, drives the tracking error to zero. A particular version of this problem is the state feedback regulator problem in which the states of the exosystem and the plant are known to the controller. Under suitable assumptions, we show that the latter problem is solvable if and only if a pair of algebraic equations, called the regulator equations, is solvable. We derive conditions, in terms of the transfer function of the plant and eigenvalues of the exosystem, for the solvability of the regulator equations. Three examples illustrating the theory are presented.

KW - Infinite-dimensional exosystem

KW - regulator equations

KW - state feedback controller

KW - unbounded control and observation operators

UR - http://www.scopus.com/inward/record.url?scp=84904763158&partnerID=8YFLogxK

U2 - 10.1109/TAC.2014.2326491

DO - 10.1109/TAC.2014.2326491

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AN - SCOPUS:84904763158

SN - 0018-9286

VL - 59

SP - 2708

EP - 2723

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 10

M1 - 6819817

ER -