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# Open Problems in Mathematical Systems and Control Theory

## Overview

System and Control theory is one of the most exciting areas of contemporary engineering mathematics. From the analysis of Watt's steam engine governor - which enabled the Industrial Revolution - to the design of controllers for consumer items, chemical plants and modern aircraft, the area has always drawn from a broad range of tools. It has provided many challenges and possibilities for interaction between engineering and established areas of 'pure' and 'applied' mathematics. This impressive volume collects a discussion of more than fifty open problems which touch upon a variety of subfields, including: chaotic observers, nonlinear local controlability, discrete event and hybrid systems, neural network learning, matrix inequalities, Lyapunov exponents, and many other issues. Proposed and explained by leading researchers, they are offered with the intention of generating further work, as well as inspiration for many other similar problems which may naturally arise from them. With extensive references, this book will be a useful reference source - as well as an excellent addendum to the textbooks in the area.

## Product Details

ISBN-13: | 9781447112075 |
---|---|

Publisher: | Springer London |

Publication date: | 10/12/2011 |

Series: | Communications and Control Engineering Series |

Edition description: | Softcover reprint of the original 1st ed. 1999 |

Pages: | 289 |

Product dimensions: | 6.10(w) x 9.25(h) x 0.03(d) |

## Read an Excerpt

System and Control theory is one of the most exciting areas of contemporary engineering mathematics. From the analysis of Watt's steam engine governor - which enabled the Industrial Revolution - to the design of controllers for consumer items, chemical plants and modern aircraft, the area has always drawn from a broad range of tools. It has provided many challenges and possibilities for interaction between engineering and established areas of 'pure' and 'applied' mathematics. This impressive volume collects a discussion of more than fifty open problems which touch upon a variety of subfields, including: chaotic observers, nonlinear local controlability, discrete event and hybrid systems, neural network learning, matrix inequalities, Lyapunov exponents, and many other issues. Proposed and explained by leading researchers, they are offered with the intention of generating further work, as well as inspiration for many other similar problems which may naturally arise from them. With extensive references, this book will be a useful reference source - as well as an excellent addendum to the textbooks in the area.

## First Chapter

System and Control theory is one of the most exciting areas of contemporary engineering mathematics. From the analysis of Watt's steam engine governor - which enabled the Industrial Revolution - to the design of controllers for consumer items, chemical plants and modern aircraft, the area has always drawn from a broad range of tools. It has provided many challenges and possibilities for interaction between engineering and established areas of 'pure' and 'applied' mathematics. This impressive volume collects a discussion of more than fifty open problems which touch upon a variety of subfields, including: chaotic observers, nonlinear local controlability, discrete event and hybrid systems, neural network learning, matrix inequalities, Lyapunov exponents, and many other issues. Proposed and explained by leading researchers, they are offered with the intention of generating further work, as well as inspiration for many other similar problems which may naturally arise from them. With extensive references, this book will be a useful reference source - as well as an excellent addendum to the textbooks in the area.

## Table of Contents

- 1: Uniform asymptotic stability of linear time-varying systems
- Dirk Aeyels, Joan Peuteman
- 2: Positive system realizations
- Brian D. O. Anderson
- 3: System approximation in the 2-norm
- A. C. Antoulas
- 4: Is it possible to recognize local controllability in a finite number of differentiations?
- Andrei A. Agrachev
- 5: Open problems in sequential parametric estimation
- Er-Wei Bai, Roberto Tempo, Yinyu Ye
- 6: Conditions for the existence and uniqueness of optimal matrix scalings
- Venkataramanan Balakrishnan
- 7: Matrix inequality conditions for canonical factorization of rational transfer function matrices
- Venkataramanan Balakrishnan
- 8: Open problems in l(subscript 1) optimal control
- Bassam Bamieh, Munther A. Dahleh
- 9: Efficient neural network learning
- Peter L. Bartlett
- 10: Mechanical feedback control systems
- Anthony M. Bloch, Naomi Ehrich Leonard, Jerrold E. Marsden
- 11: Three problems on the decidability and complexity of stability
- Vincent D. Blondel, John N. Tsitsiklis
- 12: Simultaneous stabilization of linear systems and interpolation with rational functions
- Vincent D. Blondel
- 13: Forbidden state control synthesis for timed Petri net models
- R. K. Boel, G. Stremersch
- 14: On matrix mortality in low dimensions
- Olivier Bournez, Michael Branicky
- 15: Entropy and random feedback
- Stephen P. Boyd
- 16: A stabilization problem
- Roger Brockett
- 17: Spectral factorization of a spectral density with arbitrary delays
- Frank M. Callier, Joseph J. Winkin
- 18: Lyapunov exponents and robust stabilization
- F. Colonius, D. Hinrichsen, F. Wirth
- 19: Regular spectral factorizations
- Ruth F. Curtain, Olof J. Staffans
- 20: Convergence of an algorithm for the Riemannian SVD
- Bart De Moor
- 21: Some open questions related to flat nonlinear systems
- Michel Fliess, Jean Levine, Philippe Martin (et al.)
- 22: Approximation of complex (mu)
- Minyue Fu
- 23: Spectral value sets of infinite-dimensional systems
- E. Gallestey, D. Hinrichsen, A. J. Pritchard
- 24: Selection of the number of inputs and states
- Christiaan Heij
- 25: Input-output gains of switched linear systems
- J. P. Hespanha, A. S. Morse
- 26: Robust stability of linear stochastic systems
- D. Hinrichsen, A. J. Pritchard
- 27: Monotonicity of performance with respect to its specification in H(superscript (infinity)) control
- Hidenori Kimura
- 28: Stable estimates in equation error identification: An open problem
- Roberto Lopez-Valcarce, Soura Dasgupta
- 29: Elimination of latent variables in real differential algebraic systems
- Iven Mareels, Jan C. Willems
- 30: How conservative is the circle criterion?
- Alexandre Megretski
- 31: On chaotic observer design
- Henk Nijmeijer
- 32: The minimal realization problem in the max-plus algebra
- Geert Jan Olsder, Bart De Schutter
- 33: Input design for worst-case identification
- Jonathan R. Partington
- 34: Max-plus-times linear systems
- Max Plus
- 35: Closed-loop identification and self-tuning
- Jan Willem Polderman
- 36: To estimate the L(subscript 2)-gain of two dynamic systems
- Anders Rantzer
- 37: Open problems in the area of pole placement
- Joachim Rosenthal, Jan C. Willems
- 38: An optimal control theory for systems defined over finite rings
- Joachim Rosenthal
- 39: Re-initialization in discontinuous systems
- J. M. Schumacher
- 40: Control-Lyapunov functions
- Eduardo D. Sontag
- 41: Spectral Nevanlinna-Pick Interpolation
- Allen R. Tannenbaum
- 42: Phase-sensitive structured singular value
- Andre L. Tits, V. Balakrishnan
- 43: Conservatism of the standard upper bound test: Is sup((mu)/(mu)) finite? Is it bounded by 2?
- Onur Toker, Bram de Jager
- 44: When does the algebraic Riccati equation have a negative semi-definite solution?
- Harry L. Trentelman
- 45: Representing a nonlinear input-output differential equation as an input-state-output system
- A. J. van der Schaft
- 46: Shift policies in QR-like algorithms and feedback control of self-similar flows
- Paul Van Dooren, Rodolphe Sepulchre
- 47: Equivalences of discrete-event systems and of hybrid systems
- J. H. van Schuppen
- 48: Covering numbers for input-output maps realizable by neural networks
- M. Vidyasagar
- 49: A powerful generalization of the Carleson measure theorem?
- George Weiss
- 50: Lyapunov theory for high order differential systems
- Jan C. Willems
- 51: Performance lower bound for a sampled-data signal reconstruction
- Yutaka Yamamoto, Shinji Hara
- 52: Coprimeness of factorizations over a ring of distributions
- Yutaka Yamamoto
- 53: Where are the zeros located?
- Hans Zwart
- Index

## Reading Group Guide

- 1: Uniform asymptotic stability of linear time-varying systems
- Dirk Aeyels, Joan Peuteman
- 2: Positive system realizations
- Brian D. O. Anderson
- 3: System approximation in the 2-norm
- A. C. Antoulas
- 4: Is it possible to recognize local controllability in a finite number of differentiations?
- Andrei A. Agrachev
- 5: Open problems in sequential parametric estimation
- Er-Wei Bai, Roberto Tempo, Yinyu Ye
- 6: Conditions for the existence and uniqueness of optimal matrix scalings
- Venkataramanan Balakrishnan
- 7: Matrix inequality conditions for canonical factorization of rational transfer function matrices
- Venkataramanan Balakrishnan
- 8: Open problems in l(subscript 1) optimal control
- Bassam Bamieh, Munther A. Dahleh
- 9: Efficient neural network learning
- Peter L. Bartlett
- 10: Mechanical feedback control systems
- Anthony M. Bloch, Naomi Ehrich Leonard, Jerrold E. Marsden
- 11: Three problems on the decidability and complexity of stability
- Vincent D. Blondel, John N. Tsitsiklis
- 12: Simultaneous stabilization of linear systems and interpolation with rational functions
- Vincent D. Blondel
- 13: Forbidden state control synthesis for timed Petri net models
- R. K. Boel, G. Stremersch
- 14: On matrix mortality in low dimensions
- Olivier Bournez, Michael Branicky
- 15: Entropy and random feedback
- Stephen P. Boyd
- 16: A stabilization problem
- Roger Brockett
- 17: Spectral factorization of a spectral density with arbitrary delays
- Frank M. Callier, Joseph J. Winkin
- 18: Lyapunov exponents and robust stabilization
- F. Colonius, D. Hinrichsen, F. Wirth
- 19: Regular spectral factorizations
- Ruth F. Curtain, Olof J. Staffans
- 20: Convergence of an algorithm for the Riemannian SVD
- Bart De Moor
- 21: Some open questions related to flat nonlinear systems
- Michel Fliess, Jean Levine, Philippe Martin (et al.)
- 22: Approximation of complex (mu)
- Minyue Fu
- 23: Spectral value sets of infinite-dimensional systems
- E. Gallestey, D. Hinrichsen, A. J. Pritchard
- 24: Selection of the number of inputs and states
- Christiaan Heij
- 25: Input-output gains of switched linear systems
- J. P. Hespanha, A. S. Morse
- 26: Robust stability of linear stochastic systems
- D. Hinrichsen, A. J. Pritchard
- 27: Monotonicity of performance with respect to its specification in H(superscript (infinity)) control
- Hidenori Kimura
- 28: Stable estimates in equation error identification: An open problem
- Roberto Lopez-Valcarce, Soura Dasgupta
- 29: Elimination of latent variables in real differential algebraic systems
- Iven Mareels, Jan C. Willems
- 30: How conservative is the circle criterion?
- Alexandre Megretski
- 31: On chaotic observer design
- Henk Nijmeijer
- 32: The minimal realization problem in the max-plus algebra
- Geert Jan Olsder, Bart De Schutter
- 33: Input design for worst-case identification
- Jonathan R. Partington
- 34: Max-plus-times linear systems
- Max Plus
- 35: Closed-loop identification and self-tuning
- Jan Willem Polderman
- 36: To estimate the L(subscript 2)-gain of two dynamic systems
- Anders Rantzer
- 37: Open problems in the area of pole placement
- Joachim Rosenthal, Jan C. Willems
- 38: An optimal control theory for systems defined over finite rings
- Joachim Rosenthal
- 39: Re-initialization in discontinuous systems
- J. M. Schumacher
- 40: Control-Lyapunov functions
- Eduardo D. Sontag
- 41: Spectral Nevanlinna-Pick Interpolation
- Allen R. Tannenbaum
- 42: Phase-sensitive structured singular value
- Andre L. Tits, V. Balakrishnan
- 43: Conservatism of the standard upper bound test: Is sup((mu)/(mu)) finite? Is it bounded by 2?
- Onur Toker, Bram de Jager
- 44: When does the algebraic Riccati equation have a negative semi-definite solution?
- Harry L. Trentelman
- 45: Representing a nonlinear input-output differential equation as an input-state-output system
- A. J. van der Schaft
- 46: Shift policies in QR-like algorithms and feedback control of self-similar flows
- Paul Van Dooren, Rodolphe Sepulchre
- 47: Equivalences of discrete-event systems and of hybrid systems
- J. H. van Schuppen
- 48: Covering numbers for input-output maps realizable by neural networks
- M. Vidyasagar
- 49: A powerful generalization of the Carleson measure theorem?
- George Weiss
- 50: Lyapunov theory for high order differential systems
- Jan C. Willems
- 51: Performance lower bound for a sampled-data signal reconstruction
- Yutaka Yamamoto, Shinji Hara
- 52: Coprimeness of factorizations over a ring of distributions
- Yutaka Yamamoto
- 53: Where are the zeros located?
- Hans Zwart
- Index

## Interviews

- 1: Uniform asymptotic stability of linear time-varying systems
- Dirk Aeyels, Joan Peuteman
- 2: Positive system realizations
- Brian D. O. Anderson
- 3: System approximation in the 2-norm
- A. C. Antoulas
- 4: Is it possible to recognize local controllability in a finite number of differentiations?
- Andrei A. Agrachev
- 5: Open problems in sequential parametric estimation
- Er-Wei Bai, Roberto Tempo, Yinyu Ye
- 6: Conditions for the existence and uniqueness of optimal matrix scalings
- Venkataramanan Balakrishnan
- 7: Matrix inequality conditions for canonical factorization of rational transfer function matrices
- Venkataramanan Balakrishnan
- 8: Open problems in l(subscript 1) optimal control
- Bassam Bamieh, Munther A. Dahleh
- 9: Efficient neural network learning
- Peter L. Bartlett
- 10: Mechanical feedback control systems
- Anthony M. Bloch, Naomi Ehrich Leonard, Jerrold E. Marsden
- 11: Three problems on the decidability and complexity of stability
- Vincent D. Blondel, John N. Tsitsiklis
- 12: Simultaneous stabilization of linear systems and interpolation with rational functions
- Vincent D. Blondel
- 13: Forbidden state control synthesis for timed Petri net models
- R. K. Boel, G. Stremersch
- 14: On matrix mortality in low dimensions
- Olivier Bournez, Michael Branicky
- 15: Entropy and random feedback
- Stephen P. Boyd
- 16: A stabilization problem
- Roger Brockett
- 17: Spectral factorization of a spectral density with arbitrary delays
- Frank M. Callier, Joseph J. Winkin
- 18: Lyapunov exponents and robust stabilization
- F. Colonius, D. Hinrichsen, F. Wirth
- 19: Regular spectral factorizations
- Ruth F. Curtain, Olof J. Staffans
- 20: Convergence of an algorithm for the Riemannian SVD
- Bart De Moor
- 21: Some open questions related to flat nonlinear systems
- Michel Fliess, Jean Levine, Philippe Martin (et al.)
- 22: Approximation of complex (mu)
- Minyue Fu
- 23: Spectral value sets of infinite-dimensional systems
- E. Gallestey, D. Hinrichsen, A. J. Pritchard
- 24: Selection of the number of inputs and states
- Christiaan Heij
- 25: Input-output gains of switched linear systems
- J. P. Hespanha, A. S. Morse
- 26: Robust stability of linear stochastic systems
- D. Hinrichsen, A. J. Pritchard
- 27: Monotonicity of performance with respect to its specification in H(superscript (infinity)) control
- Hidenori Kimura
- 28: Stable estimates in equation error identification: An open problem
- Roberto Lopez-Valcarce, Soura Dasgupta
- 29: Elimination of latent variables in real differential algebraic systems
- Iven Mareels, Jan C. Willems
- 30: How conservative is the circle criterion?
- Alexandre Megretski
- 31: On chaotic observer design
- Henk Nijmeijer
- 32: The minimal realization problem in the max-plus algebra
- Geert Jan Olsder, Bart De Schutter
- 33: Input design for worst-case identification
- Jonathan R. Partington
- 34: Max-plus-times linear systems
- Max Plus
- 35: Closed-loop identification and self-tuning
- Jan Willem Polderman
- 36: To estimate the L(subscript 2)-gain of two dynamic systems
- Anders Rantzer
- 37: Open problems in the area of pole placement
- Joachim Rosenthal, Jan C. Willems
- 38: An optimal control theory for systems defined over finite rings
- Joachim Rosenthal
- 39: Re-initialization in discontinuous systems
- J. M. Schumacher
- 40: Control-Lyapunov functions
- Eduardo D. Sontag
- 41: Spectral Nevanlinna-Pick Interpolation
- Allen R. Tannenbaum
- 42: Phase-sensitive structured singular value
- Andre L. Tits, V. Balakrishnan
- 43: Conservatism of the standard upper bound test: Is sup((mu)/(mu)) finite? Is it bounded by 2?
- Onur Toker, Bram de Jager
- 44: When does the algebraic Riccati equation have a negative semi-definite solution?
- Harry L. Trentelman
- 45: Representing a nonlinear input-output differential equation as an input-state-output system
- A. J. van der Schaft
- 46: Shift policies in QR-like algorithms and feedback control of self-similar flows
- Paul Van Dooren, Rodolphe Sepulchre
- 47: Equivalences of discrete-event systems and of hybrid systems
- J. H. van Schuppen
- 48: Covering numbers for input-output maps realizable by neural networks
- M. Vidyasagar
- 49: A powerful generalization of the Carleson measure theorem?
- George Weiss
- 50: Lyapunov theory for high order differential systems
- Jan C. Willems
- 51: Performance lower bound for a sampled-data signal reconstruction
- Yutaka Yamamoto, Shinji Hara
- 52: Coprimeness of factorizations over a ring of distributions
- Yutaka Yamamoto
- 53: Where are the zeros located?
- Hans Zwart
- Index

## Recipe

- 1: Uniform asymptotic stability of linear time-varying systems
- Dirk Aeyels, Joan Peuteman
- 2: Positive system realizations
- Brian D. O. Anderson
- 3: System approximation in the 2-norm
- A. C. Antoulas
- 4: Is it possible to recognize local controllability in a finite number of differentiations?
- Andrei A. Agrachev
- 5: Open problems in sequential parametric estimation
- Er-Wei Bai, Roberto Tempo, Yinyu Ye
- 6: Conditions for the existence and uniqueness of optimal matrix scalings
- Venkataramanan Balakrishnan
- 7: Matrix inequality conditions for canonical factorization of rational transfer function matrices
- Venkataramanan Balakrishnan
- 8: Open problems in l(subscript 1) optimal control
- Bassam Bamieh, Munther A. Dahleh
- 9: Efficient neural network learning
- Peter L. Bartlett
- 10: Mechanical feedback control systems
- Anthony M. Bloch, Naomi Ehrich Leonard, Jerrold E. Marsden
- 11: Three problems on the decidability and complexity of stability
- Vincent D. Blondel, John N. Tsitsiklis
- 12: Simultaneous stabilization of linear systems and interpolation with rational functions
- Vincent D. Blondel
- 13: Forbidden state control synthesis for timed Petri net models
- R. K. Boel, G. Stremersch
- 14: On matrix mortality in low dimensions
- Olivier Bournez, Michael Branicky
- 15: Entropy and random feedback
- Stephen P. Boyd
- 16: A stabilization problem
- Roger Brockett
- 17: Spectral factorization of a spectral density with arbitrary delays
- Frank M. Callier, Joseph J. Winkin
- 18: Lyapunov exponents and robust stabilization
- F. Colonius, D. Hinrichsen, F. Wirth
- 19: Regular spectral factorizations
- Ruth F. Curtain, Olof J. Staffans
- 20: Convergence of an algorithm for the Riemannian SVD
- Bart De Moor
- 21: Some open questions related to flat nonlinear systems
- Michel Fliess, Jean Levine, Philippe Martin (et al.)
- 22: Approximation of complex (mu)
- Minyue Fu
- 23: Spectral value sets of infinite-dimensional systems
- E. Gallestey, D. Hinrichsen, A. J. Pritchard
- 24: Selection of the number of inputs and states
- Christiaan Heij
- 25: Input-output gains of switched linear systems
- J. P. Hespanha, A. S. Morse
- 26: Robust stability of linear stochastic systems
- D. Hinrichsen, A. J. Pritchard
- Hidenori Kimura
- 28: Stable estimates in equation error identification: An open problem
- Roberto Lopez-Valcarce, Soura Dasgupta
- 29: Elimination of latent variables in real differential algebraic systems
- Iven Mareels, Jan C. Willems
- 30: How conservative is the circle criterion?
- Alexandre Megretski
- 31: On chaotic observer design
- Henk Nijmeijer
- 32: The minimal realization problem in the max-plus algebra
- Geert Jan Olsder, Bart De Schutter
- 33: Input design for worst-case identification
- Jonathan R. Partington
- 34: Max-plus-times linear systems
- Max Plus
- 35: Closed-loop identification and self-tuning
- Jan Willem Polderman
- 36: To estimate the L(subscript 2)-gain of two dynamic systems
- Anders Rantzer
- 37: Open problems in the area of pole placement
- Joachim Rosenthal, Jan C. Willems
- 38: An optimal control theory for systems defined over finite rings
- Joachim Rosenthal
- 39: Re-initialization in discontinuous systems
- J. M. Schumacher
- 40: Control-Lyapunov functions
- Eduardo D. Sontag
- 41: Spectral Nevanlinna-Pick Interpolation
- Allen R. Tannenbaum
- 42: Phase-sensitive structured singular value
- Andre L. Tits, V. Balakrishnan
- 43: Conservatism of the standard upper bound test: Is sup((mu)/(mu)) finite? Is it bounded by 2?
- Onur Toker, Bram de Jager
- 44: When does the algebraic Riccati equation have a negative semi-definite solution?
- Harry L. Trentelman
- 45: Representing a nonlinear input-output differential equation as an input-state-output system
- A. J. van der Schaft
- 46: Shift policies in QR-like algorithms and feedback control of self-similar flows
- Paul Van Dooren, Rodolphe Sepulchre
- 47: Equivalences of discrete-event systems and of hybrid systems
- J. H. van Schuppen
- 48: Covering numbers for input-output maps realizable by neural networks
- M. Vidyasagar
- 49: A powerful generalization of the Carleson measure theorem?
- George Weiss
- 50: Lyapunov theory for high order differential systems
- Jan C. Willems
- 51: Performance lower bound for a sampled-data signal reconstruction
- Yutaka Yamamoto, Shinji Hara
- 52: Coprimeness of factorizations over a ring of distributions
- Yutaka Yamamoto
- 53: Where are the zeros located?
- Hans Zwart
- Index