University of Groningen A geometric approach to differential-algebraic systems Megawati, Noorma

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University of Groningen

A geometric approach to differential-algebraic systems

Megawati, Noorma

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Publication date: 2017

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Megawati, N. (2017). A geometric approach to differential-algebraic systems: from bisimulation to control by interconnection. University of Groningen.

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512350-L-sub01-bw-Megawati 512350-L-sub01-bw-Megawati 512350-L-sub01-bw-Megawati 512350-L-sub01-bw-Megawati Processed on: 10-8-2017 Processed on: 10-8-2017 Processed on: 10-8-2017

Processed on: 10-8-2017 PDF page: 1PDF page: 1PDF page: 1PDF page: 1

A GEOMETRIC APPROACH TO

DIFFERENTIAL-ALGEBRAIC SYSTEMS

FROM BISIMULATION TO CONTROL BY INTERCONNECTION

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The research described in this dissertation has been carried out at the Johann Bernoulli Institute for Mathematics and Computer Science (JBI), Faculty of Mathe-matics and Natural Sciences, University of Groningen, The Netherlands.

This dissertation has been completed in partial fulﬁlment of the requirements of the Dutch Institute of Systems and Control (DISC) for graduate study.

The work presented in this dissertation is supported by the Directorate General of Higher Education (DIKTI), The Ministry of Research, Technology, and Higher Education of Indonesia.

A geometric approach to differential-algebraic systems: From bisimulation to control by interconnection Noorma Yulia Megawati

PhD Thesis University of Groningen Cover by Raymond Nainggolan Printed by Ipskamp Printing

ISBN (printed version): 978-94-028-0731-8 ISBN (electronic version): 978-94-034-0052-5

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A geometric approach to

differential-algebraic systems:

From bisimulation to control by interconnection

PhD thesis

to obtain the degree of PhD at the University of Groningen

on the authority of the Rector Magniﬁcus Prof. E. Sterken

and in accordance with the decision by the College of Deans. This thesis will be defended in public on Friday 15 September 2017 at 11.00 hours

by

Noorma Yulia Megawati

born on 29 July 1986 in Sleman, Indonesia

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Processed on: 10-8-2017 PDF page: 4PDF page: 4PDF page: 4PDF page: 4 Supervisors

Prof. A.J. van der Schaft Prof. H.L. Trentelman

Assessment committee

Prof. M.K. C¸amlıbel Prof. J.M. Schumacher Prof. S. Weiland

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To Ibu and Bapak (Alm.)

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Acknowledgments

Alhamdulillah, All praise to Allah SWT. Undertaking these recent four years of PhD is quite challenging; thus, I would like to take the opportunity to express my sincere gratitude to people who supported me during my PhD life.

First of all, I would like to deliver my gratitude to my supervisor Prof. Arjan van der Schaft, for kindly giving me the opportunity to pursue my education as a PhD candidate in his department. I thank him for his endless support, supervision, and guidance during my study. I owe him my gratitude for teaching me how to conduct research through the stimulating weekly discussions. I thank him also for his patience in helping me to perfect ionize my English-mathematics skills.

I would like to thank Prof. Harry Trentelman for helping me at various moments in these last four years as well as to Prof. Bayu Jayawardhana and Tim Zwaagstra who interviewed me for the PhD position.

In addition, I would also like to express my gratitude to Prof. Kanat C¸amlıbel, Prof. Hans Schumacher, and Prof. Siep Weiland for reading the ﬁnal thesis draft and subsequently for supplying me with comments and suggestions. Their inputs were invaluable for improving my thesis.

Next, I would like to thank to my colleagues of the SCAA group, you have provided a wonderful environment for me during the past four years. I also thank to Ineke and Esmee for their help regarding to all kinds of administrative affairs. Rully and Zaki, I thank you for our fruitful discussion when struggling with the DISC courses. To Desti, thanks for always willing to listen to all my stories.

Life in this country would not be colorful without my Indonesian friends, here in Groningen. Mbak Mala, thank you for always supporting me and giving me advice when I needed, for our great adventure in traveling and shopping tour and for your kindness to be my paranymph. Mbak Vera, I thank you for also being my paranymph and I would not forget how you took my mind of my research with the photography session we ever had. We always tried to ﬁnd beautiful spots of Groningen to take pictures. To Mbak Nur Qomariyah, Mbak Ira, Mbak Ira Sianturi,

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Mbak Ima, Salma, I thank you for sharing a pleasant time during my 4 years of life in Groningen. To my cousin, Mbak Tiwi, ﬁnally you followed me to pursue your PhD in Netherlands (Amsterdam) and I wish you success for your study!

To the people of Indonesia, I would like to thank especially the Indonesian Directorate General of Higher Education (DIKTI) for providing me the ﬁnancial support to undertake my PhD study in the Netherlands. I would like to express my gratitude to the Department of Mathematics, Universitas Gadjah Mada, Yogyakarta, Indonesia, my almamater and my institution where I work. Bu Salmah and Bu Indah, I owe them my gratitude for introducing me with systems and control theory. Bu Salmah, thank you for helping me with the Indonesian summary. To Mbak Dewi, Mbak Nur, Rianti, Zenith and Nanang, thank you for everything!

Last but not least, my special thanks to my family, my mother (Ibu) and my brothers. Untuk Ibu, terima kasih atas semua doa dan supportnya kepada ananda selama ananda menempuh pendidikan di Belanda. Terima kasih atas semua nase-hatnya agar selalu kuat menjalani kehidupan disini. Untuk adik-adikku, Agung dan Jeffri, terima kasih untuk supportnya. I dedicate this PhD award to you.

Groningen, July 2017

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List of notations

R Real numbers

C Complex numbers

N {0, 1, 2, · · · } the set of natural numbers Rn _{n-dimensional linear space}

Rn×m _{the space of n × m real constant matrices}

C∞ _{the space of inﬁnitely differentiable functions}

im M image of matrix M

ker M kernel of matrix M

MT _{transpose of matrix M}

M† Moore-Penrose pseudoinverse of matrix M

M⊥ _{left annihilator of matrix M}

In n× n identity matrix N nilpotent matrix π canonical projection Π permutation matrix A−1_Z _{{x ∈ Z | Ax ∈ Z}} ⊕ direct sum X /S quotient space

[x]_S equivalence class of x with respect to a subspace S

end of proof

≈ bisimilar

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University of Groningen A geometric approach to differential-algebraic systems Megawati, Noorma