Publications

Book Chapters

• Controlled and conditioned invariance for polynomial and rational feedback systems
  (with C. Schilli and V. Levandovskyy) Advances in Delays and Dynamics @ Springer, Vol. 9,
  Algebraic and Symbolic Computation Methods in Dynamical Systems (2020)
• Algebraic theory of linear systems: a survey
  (with W. Seiler) Differential-Algebraic Equations Forum,
  Surveys in Differential Algebraic Equations II, 287-333 (2015)

Submitted Papers and Work in Progress

• Quotienting: a new perspective on the control of nD systems (with D. Pal),
  to appear in Proc. 9th IFAC SSSC (2025)
• Beyond the Givone-Roesser/Fornasini-Marchesini models: a universal input/state/output model for 2-D systems
  (with D. Pal and P. Rocha), submitted to MCRF, September 2024

Journal Articles

1. The graded Hautus test of controllability for 2-D systems (with D. Pal),
   IEEE Control Systems Letters 8, 490-495 (2024)
2. Invariance of a class of semi-algebraic sets for polynomial systems with dynamic compensators
   (with T. Yuno and T. Ohtsuka), Automatica 122 (2020)
3. Attracting and natural invariant varieties for polynomial vector fields and control systems
   (with N. Kruff, C. Schilli, S. Walcher) Qualitative Theory of Dynamical Systems 19 (2020)
4. Classical quasi-steady state reduction - A mathematical characterization
   (with A. Goeke and S. Walcher) Physica D 345, 11-26 (2017)
5. Determining small parameters for quasi-steady state
   (with A. Goeke and S. Walcher) Journal of Differential Equations 259, 1149-1180 (2015)
6. nD methods for 1D parameter-dependent systems
   (with S. Walcher) Multidimensional Systems and Signal Processing 26, 1097-1108 (2015)
7. Controlled Invariant Hypersurfaces of Polynomial Control Systems
   (with S. Walcher) Qualitative Theory of Dynamical Systems 11, 145-158 (2012)
8. Computing Quasi-steady State Reductions (with A. Goeke et al.)
   Journal of Mathematical Chemistry 50, 1495-1513 (2012)
9. A Note on the Kinetics of Suicide Substrates (with A. Goeke et al.)
   Journal of Mathematical Chemistry 50, 1373-1377 (2012)
10. Finite Multidimensional Behaviors (with L. Wagner)
    Multidimensional Systems and Signal Processing 23, 5-15 (2012)
11. Exact Linear Modeling using Ore Algebras (with V. Levandovskyy and K. Schindelar)
    Journal of Symbolic Computation 46, 1189-1204 (2011)
12. Exact Linear Modeling with Polynomial Coefficients
    (with V. Levandovskyy and K. Schindelar)
    Multidimensional Systems and Signal Processing 22, 55-65 (2011)
13. On the Inverse Syzygy Problem (with W. Seiler and M. Hausdorf)
    Communications in Algebra 38, 2037-2047 (2010)
14. On Multidimensional Convolutional Codes and Controllability Properties
    of Multidimensional Systems over Finite Rings
    Asian Journal of Control 12, 119-126 (2010)
15. The Discrete Multidimensional MPUM
    Multidimensional Systems and Signal Processing 19, 307-321 (2008)
16. Behavioral Systems Theory: A Survey
    Applied Mathematics and Computer Science 18, 265-270 (2008)
17. Qualitative Properties and Stabilizability of a Model for Blood Thrombin Formation
    (with S. Orfao et al.) Mathematical Analysis and Applications 346, 218-226 (2008)
18. Discrete Multidimensional Systems over Z/nZ
    Systems and Control Letters 56, 702-708 (2007)
19. Controllability and Extendibility of Continuous Multidimensional Behaviors
    (with P. Rocha) Multidimensional Systems and Signal Processing 17, 97-106 (2006)
20. An Algebraic Analysis Approach to Linear Time-varying Systems
    IMA Journal of Mathematical Control and Information 23, 113-126 (2006)
21. Characteristic Frequencies, Polynomial-exponential Trajectories,
    and Linear Exact Modeling with Multidimensional Behaviors
    SIAM Journal on Control and Optimization 44, 1148-1163 (2005)
22. Strong Controllability and Extendibility of Discrete Multidimensional Behaviors
    (with P. Rocha) Systems and Control Letters 54, 375-380 (2005)
23. Multidimensional Behaviors: An Algebraic Approach to Control Theory for PDE
    International Journal of Control 77, 812-820 (2004)
24. On the Extension of Solutions of Systems of Linear Constant PDE
    Systems and Control Letters 50, 127-133 (2003)
25. A Constructive Solution to Interconnection and Decomposition Problems
    (with V. Lomadze) SIAM Journal on Control and Optimization 40, 1072-1086 (2001)
26. Extension Modules in Behavioral Linear Systems Theory
    Multidimensional Systems and Signal Processing 12, 309-327 (2001)
27. First-order Representations of Discrete Linear Multidimensional Systems
    Multidimensional Systems and Signal Processing 11, 359-380 (2000)
28. Coprime Factorizations of Multivariate Rational Matrices
    Mathematics of Control, Signals, and Systems 13, 125-139 (2000)
29. On Strict System Equivalence for Multidimensional Systems
    International Journal of Control 73, 495-504 (2000)
30. Fractional Representations of Linear Systems
    (with V. Lomadze) Systems and Control Letters 39, 275-281 (2000)
31. Notes on the Definition of Behavioural Controllability
    (with J. Wood) Systems and Control Letters 37, 31-37 (1999)
32. LFT Representations of Parametrized Polynomial Systems
    IEEE Trans. Circuits and Systems I 46, 410-417 (1999)
33. A Balanced Canonical Form for Discrete-Time Minimal Systems
    (with J. Hoffmann and D. Prätzel-Wolters)
    Linear Algebra and Its Applications 277, 63-81 (1998)
34. Primeness of Multivariate Polynomial Matrices
    Systems and Control Letters 29, 139-146 (1996)
35. The Canonical Cauchy Problem for Linear Systems
    of Partial Difference Equations (with U. Oberst)
    Acta Applicandae Mathematicae 31, 249-273 (1993)

Proceedings

1. Linear dynamical systems over finite rings (with Y. Rohde),
   Proc. Math. Theory Networks Systems (MTNS 2024), IFAC PapersOnLine 58-17 (2024)
2. Controlled invariant varieties for second order polynomial control systems
   (with M. Harms and M. Herty), Proc. Math. Theory Networks Systems (MTNS 2024), IFAC PapersOnLine 58-17 (2024)
3. Invariant sets for a class of nonlinear control systems tractable by symbolic computation
   (with M. Harms and C. Schilli), Proc. IFAC World Congress, IFAC PapersOnLine 56-2 (2023)
   (IFAC Congress Interactive Paper Prize)
4. On d-collision-free systems (with M. Harms, S. Bamberger, M. Herty),
   Proc. 8th IFAC Symposium System Structure and Control (SSSC), IFAC PapersOnLine 55-34 (2022)
   (IFAC SSSC Young Author Award for M. Harms)
5. Disturbance decoupling for polynomial systems
   (with M. Harms), Proc. Math. Theory Networks Systems (MTNS), IFAC PapersOnLine 54-9 (2021)
6. Computing the cycle structure of finite linear systems
   (with H. Giese), Proc. IFAC World Congress, Berlin (2020)
7. Collision-free dynamical systems
   (with M. Herty) Proc. 7th IFAC Symposium System Structure and Control (SSSC), Sinaia (2019)
8. Controlled invariance for 1D and 2D time-varying nonlinear control systems
   (with T. Yuno) Proc. Math. Theory Networks Systems (MTNS), Hong Kong (2018)
9. Controlled invariance for nonlinear Roesser models
   (with C. Schilli) Proc. 10th Int. Workshop on Multidimensional Systems (NDS), Zielona Gora (2017)
10. Polynomial control systems: Invariant sets given by algebraic equations/inequations
    (with M. Harms and C. Schilli) Proc. IFAC World Congress, Toulouse (2017)
11. Controlled and conditioned invariant varieties for polynomial control systems with rational feedback
    (with C. Schilli and V. Levandovskyy) Proc. Math. Theory Networks Systems (MTNS), Minneapolis (2016)
12. State representations of finitely generated nD behaviors over rings
    Proc. 9th Int. Workshop on Multidimensional Systems (NDS), Vila Real (2015)
13. Quasi-steady state -- Intuition, perturbation theory and algorithmic algebra
    (with A. Goeke and S. Walcher) Proc. 17th Int. Workshop on Computer Algebra in
    Scientific Computing (CASC), Springer Lecture Notes in Computer Science 9301 (2015)
14. Controlled and conditioned invariant varieties for polynomial control systems
    (with C. Schilli and V. Levandovskyy) Proc. Math. Theory Networks Systems (MTNS), Groningen (2014)
15. A solution formula for finite-dimensional systems (with B. Belayneh)
    Proc. 8th Int. Workshop on Multidimensional Systems (NDS), Erlangen (2013)
16. On periodic solutions of 2-d linear difference equations
    Proc. 7th Int. Workshop on Multidimensional Systems (NDS), Poitiers (2011)
17. The Inverse Syzygy Problem in Algebraic Systems Theory
    (with W. Seiler) PAMM 10 (2010)
18. Controlled Invariant Varieties of Polynomial Control Systems
    (with S. Walcher and F. Güclü)
    Proc. Math. Theory Networks Systems (MTNS), Budapest (2010)
19. On Periodic Solutions of Linear Difference Equations
    Proc. Math. Theory Networks Systems (MTNS), Budapest (2010)
20. Strongly Autonomous Behaviors over Finite Rings
    Proc. 6th Int. Workshop on Multidimensional Systems (NDS), Thessaloniki (2009)
21. Linear Exact Modeling with Variable Coefficients
    (with K. Schindelar and V. Levandovskyy)
    Proc. Math. Theory of Networks and Systems (MTNS), Blacksburg (2008)
22. State Representations of Time-varying Linear Systems
    Radon Series on Computational and Applied Mathematics 3, 235-251 (2007)
23. Obstructions to Genericity in the Study of Parametric Problems in Control Theory
    (with V. Levandovskyy)
    Radon Series on Computational and Applied Mathematics 3, 127-149 (2007)
24. Autonomy Properties of Multidimensional Linear Systems over Rings
    Proc. 5th Int. Workshop on Multidimensional Systems (NDS), Aveiro (2007)
25. Linear Exact Modeling from Multivariate Data
    GAMM-Jahrestagung 2006, Berlin, PAMM 6 (2006)
26. First Order Representations of Time-varying Linear Systems
    Proc. IEEE Int. Symp. Computer-Aided Control Systems Design, Munich (2006)
27. Algebraic Systems Theory and Computer Algebraic Methods for Some Classes
    of Linear Control Systems (with V. Levandovskyy)
    Proc. Math. Theory of Networks and Systems (MTNS), Kyoto (2006)
28. Recursive Computation of the Multidimensional MPUM
    Proc. Math. Theory of Networks and Systems (MTNS), Kyoto (2006)
29. Computer Algebraic Methods for the Structural Analysis
    of Linear Control Systems (with V. Levandovskyy)
    GAMM-Jahrestagung 2005, Luxemburg, PAMM 5 (2005)
30. An Algebraic Analysis Approach to Linear Time-varying Behaviors
    Proc. 16th IFAC World Congress, Prag (2005)
31. Poles, Polynomial-exponential Trajectories and the MPUM
    Proc. Math. Theory of Networks and Systems (MTNS), Leuven (2004)
32. Strong Controllability of Continuous Multidimensional Behaviors
    (with P. Rocha)
    Proc. Math. Theory of Networks and Systems (MTNS), Leuven (2004)
33. Autonomy, Controllability, and Extension Modules
    GAMM-Jahrestagung 2002, Augsburg, PAMM 2 (2003)
34. The Problem of Causality in Multidimensional Systems Theory
    Proc. 8th IEEE Conference on Methods and Models
    in Automation and Robotics (MMAR), Stettin (2002)
35. Over-determined Systems
    Proc. Math. Theory of Networks and Systems (MTNS), South Bend (2002)
36. On the Lattice of Behaviours
    Proc. 6th European Control Conference (ECC), Porto (2001)
37. Some Applications of Gröbner Bases in Multidimensional Systems Theory
    GAMM-Jahrestagung 2000, Göttingen, ZAMM 81 (2001)
38. Stabilization of multidimensional systems
    Proc. WCNA 2000, Catania (2000)
39. Control and Interconnection Revisited: The Linear Multidimensional Case
    (with V. Lomadze) Proc. 2nd International Workshop on
    Multidimensional Systems (NDS), Czocha Castle (2000)
40. Partial Differential Equations of Krull Dimension Zero
    (with V. Lomadze)
    Proc. Math. Theory of Networks and Systems (MTNS), Perpignan (2000)
41. First-order Representations of Multidimensional Behaviours
    Proc. Math. Theory of Networks and Systems (MTNS), Perpignan (2000)
42. Coprime Factorization in Multidimensional Systems Theory
    GAMM-Jahrestagung 1999, Metz, ZAMM 80 (2000)
43. A balanced model reduction method for a class of matrix inversion problems
    with parametric uncertainty
    Proc. 38th IEEE Conference on Decision and Control (CDC), Phoenix (1999)
44. Notes on Strict System Equivalence: A Generalization of some Theorems of Pernebo
    to Multidimensional Systems
    Proc. 38th IEEE Conference on Decision and Control (CDC), Phoenix (1999)
45. Coprime Factorizations of Bivariate Rational Matrices
    Tagungsbericht des GAMM-Fachausschusses Dynamik und Regelungstheorie,
    Kaiserslautern, November 1998
46. Linear Fractional Representations of Polynomially Parametrized Descriptor Systems
    Proc. 3rd Portuguese Conference on Automatic Control (Controlo), Coimbra (1998)
47. Primeness of Multivariate Laurent Polynomial Matrices
    Proc. 4th European Control Conference (ECC), Brüssel (1997)
48. A Note on Controllability of Multidimensional Linear Systems
    Proc. IFAC Conference on Control of Industrial Systems (CIS), Belfort (1997)
49. Primeness Notions in Multidimensional Systems Theory
    Proc. 35th IEEE Conference on Decision and Control (CDC) (1996)
50. Computer Algebraic Methods for Multidimensional Discrete Systems
    Proc. 34th IEEE Conference on Decision and Control (CDC), New Orleans (1995)

Co-edited Special Issues

• Special Issue of Multidimensional Systems and Signal Processing
  (with A. Quadrat (Ed.))
  Volume 26, Issue 2 (2015)
• Special Issue of Multidimensional Systems and Signal Processing
  (with K. Galkowski (Ed.))
  Volume 19, Issue 3-4 (2008)
• Special Issue of Linear Algebra and Its Applications
  (with A. C. Antoulas, U. Helmke, J. Rosenthal, V. Vinnikov (Eds.))
  Volume 425, Issue 2-3 (2007)

Books

• Algebraic and Symbolic Computation Methods in Dynamical Systems
  (with A. Quadrat (Ed.))
  Advances in Delays and Dynamics @ Springer, Vol. 9 (2020)
• Algebraic Systems Theory, Behaviors, and Codes
  Shaker, Aachen (2010)
• Topics in Multidimensional Linear Systems Theory
  Springer Lecture Notes in Control and Information Sciences 256
  Springer, London (2000)
• Operators, Systems, and Linear Algebra
  (with U. Helmke and D. Prätzel-Wolters (Eds.))
  Teubner, Stuttgart (1997)

Lecture Notes and Miscellanea

• Komm. Algebra, Elem. Zahlentheorie
  Vorlesungsskripte, RWTH Aachen (2013)
• Computeralgebra
  Vorlesungsskript, RWTH Aachen (2012)
• Lineare Algebra I und II
  Vorlesungsskripte, RWTH Aachen (2011)
• Linear and nonlinear control theory: a survey
  Oberwolfach Reports 7 (2010)
• Mathematische Grundlagen
  Vorlesungsskript, RWTH Aachen (2007)
• Algebraic analysis of time-varying linear behaviors
  Oberwolfach Reports 2 (2005)
• Algebraic Systems Theory
  Berichte der AG Technomathematik 259 (2004)
• Anwendungen der Computeralgebra in der System- und Kontrolltheorie
  Computeralgebra-Rundbrief 33 (2003)
• Mathematical Modeling: An Introduction (with H. Neunzert)
  Electronic lecture notes (2003)
• Introduction to Systems and Control Theory
  Berichte der AG Technomathematik 248 (2002)
• Mathematical Theory of Neural Networks
  (with U. Helmke and D. Prätzel-Wolters)
  Berichte der AG Technomathematik 238 (2001)
• Multidimensionale Systemtheorie
  Berichte der AG Technomathematik 164 (1996)