Discrete linear repetitive processes are a distinct class of two-dimensional (2-D) linear systems with applications in areas ranging from long-wall coal cutting through to iterative learning control schemes. The feature which makes them distinct from other classes of 2-D linear systems is that information propagation in one of the two distinct directions only occurs over a finite durations. This, in turn, means that a distinct systems theory must be developed for them. In this paper, an LMI approach is used to produce highly significant new results on the stability analysis of these processes and the design of control schemes for them. These results are, in the main, for processes with singular dynamics and for those with so-called dynamic boundary conditions. Unlike other classes of 2-D linear systems, these feedback control laws have a firm physical basis, and the LMI setting is also shown to provide a (potentially) very powerful setting in which to characterize the robustness properties of these processes.published_or_final_versio

D. H. Owens

Eric Rogers

J. Lam

K. Galkowski

S. Xu

Senior Member

IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications

Rogers, E

Galkowski, K

Xu, S

Lam, J

Owens, DH

HKU Scholars Hub

LMIs - A fundamental tool in analysis and controller design for discrete linear repetitive processes

Abstract—Discrete linear repetitive processes are a distinct class of two-dimensional (2-D) linear systems with applications in areas ranging from long-wall coal cutting through to iterative learning control schemes. The feature which makes them distinct from other classes of 2-D linear systems is that information propagation in one of the two distinct directions only occurs over a finite dura-tion. This, in turn, means that a distinct systems theory must be developed for them. In this paper, an LMI approach is used to pro-duce highly significant new results on the stability analysis of these processes and the design of control schemes for them. These re-sults are, in the main, for processes with singular dynamics and for those with so-called dynamic boundary conditions. Unlike other classes of 2-D linear systems, these feedback control laws have a firm physical basis, and the LMI setting is also shown to provide a (potentially) very powerful setting in which to characterize the robustness properties of these processes. Index Terms—Linear matrix inequalities, repetitive processes, stability and control. I

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LMIs-a fundamental tool in analysis and controller design for discrete linear repetitive processes

Discrete linear repetitive processes are a distinct class of 2D linear systems with applications in areas ranging from long-wall coal cutting through to iterative learning control schemes. The feature which makes them distinct from other classes of 2D linear systems is that information propagation in one of the two independent directions only occurs over a finite duration. This, in turn, means that a distinct systems theory must be developed for them. developed. In this paper, an LMI approach is used to produce highly significant results on the stability analysis of these processes and the design of control laws for them. These new results are, in the main, for processes with singular dynamics and for those with so-called dynamic boundary conditions. Unlike other classes of 2D linear systems, these control laws have a firm physical basis, and the LMI setting is also shown to provide a firm basis on which to characterize the robustness properties of these processes

Owens, D H

Southampton (e-Prints Soton)

English

(S’86–M’86–SM’99) received the first class B.Sc. degree in mechanical engineering from the University of Manchester, Manchester, U.K. in 1983, and the M.Phil. and Ph.D. degrees in the area of control engineering, from the University of Cambridge,

[13] E.Rogers,K.Galkowski,andD.H.Owens,“Controlsystemstheoryand applications for linear repetitive processes,”

1-D model based stability analysis for a class of 2D linear systems,”

A discrete state-space model for linear image processing,”

Analysis and control of linear repetitive processes,”

Eric Rogers was born in 1956 near Dungannon. Northern Ireland, U.K. He received the undergraduate degree in mechanical engineering from The Queen’s University,

Generalized 2-D continuous-discrete linear systems with delay,”

He is the Chairman of the United Kingdom Automatic Control Council for the period 1999–2002 and is also an Independent Member of the U.K. Health and Safety Executive Nuclear Safety Committee.

He was a Lecturer at The Queen’s University from

Linear matrix inequalities in systems and control theory,”

LMI based stability analysis for discrete linear repititive processes,” in

Lyapunovinequalityand boundedreal lemma for discrete-time descriptor systems,”

Predictive optimal iterative learning control,”

received the M.S., Ph.D., and Habilitation degrees in electronics/automatic control from the

Stability analysis for linear repetitive processes,”

Stability analysis of iterative optimal control algorithms modeled as linear repetitive processes,” in

Stability problems in the control of multipass processes,”

State models and stability for2-Dfilters,”IEEETrans.CircuitsSyst.,vol.CAS-37,pp.1509–1519,

to 2000, he was a Research Associate in the Department of Mechanical Engineering, University of Hong Kong, Hong Kong. From

was born in 1968 in Zhejiang Province,

LMIs - a Fundamental Tool in Analysis and Controller Design for Discrete Linear Repetitive Processes

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LMIs - A fundamental tool in analysis and controller design for discrete linear repetitive processes

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