On the Internal Model Structure for Infinite‐Dimensional Systems: Two Common Controller Types and Repetitive Control

Immonen, Eero

doi:10.1137/050638916

Cited by 53 publications

(34 citation statements)

References 28 publications

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“…Regulator theory for infinite-dimensional linear systems with bounded control and observation operators has been significantly advanced by a group of researchers at Tampere University of Technology (Finland) who have developed a sophisticated theory of infinite-dimensional exosystems, see for instance [24], [26]- [28], [39], [40]. The state feedback regulator problem for exponentially stabilizable linear plants driven by infinite-dimensional exosystems generating periodic signals was addressed in [27].…”

Section: Introductionmentioning

confidence: 99%

“…The results in [27] were generalized in [28] by considering strongly stabilizable plants and a broader class of exosystems, and addressing both the state and error feedback regulator problems. The robustness of solutions to the error feedback regulator problem was characterized in [26] in terms of the controller having the Internal Model Structure (IMS) and in [24] in terms of the controller satisfying the G-conditions (as it is called in [39]). The recent paper Boulite et al [2] builds on the above works to address the state feedback regulator problem for polynomially stabilizable linear plants driven by infinite-dimensional exosystems.…”

Section: Introductionmentioning

confidence: 99%

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The State Feedback Regulator Problem for Regular Linear Systems

Natarajan

Gilliam

Weiss

2014

IEEE Trans. Automat. Contr.

129

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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.Index Terms-Infinite-dimensional exosystem, regulator equations, state feedback controller, unbounded control and observation operators.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The State Feedback Regulator Problem for Regular Linear Systems

Natarajan

Gilliam

Weiss

2014

IEEE Trans. Automat. Contr.

129

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“…For this system class the robust output regulation problem was investigated in Byrnes, Lauko, Gilliam, and Shubov (2000), Immonen (2007), Hämäläinen and Pohjolainen (2010), Paunonen and Pohjolainen (2010) for bounded control and observation. Therein, the first work assumes finite-dimensional signal models, whereas the latter three references also achieve output regulation for an infinite-dimensional signal process.…”

Section: Introductionmentioning

confidence: 99%

A backstepping approach to the output regulation of boundary controlled parabolic PDEs

Deutscher

2015

Automatica

132

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“…These results were generalized for infinitedimensional systems with finite-dimensional exosystems by Pohjolainen [5], Hämäläinen and Pohjolainen [6] and Rebarber and Weiss [7]. Robust regulation problem with infinitedimensional exosystem was considered in [1], [8] and [9].…”

Section: Introductionmentioning

confidence: 94%