Prof. Dr. Achim Ilchmann

address for visitors
Weimarer Str. 25 Curiebau
Room C 232
98693 Ilmenau

mailing address
Postfach 10 05 65
98684 Ilmenau

achim.ilchmann@tu-ilmenau.de

+49 3677 69-3623 (Univ.)

Merle Baur

Retired since April 2022.

Research

Professor Dr Achim Ilchmann served as Head of the ‘Analysis and Systems Theory’ group from 2000 to 2022. From 2003 to 2020 he organised the annual Elgersburg workshop on ‘Mathematical Systems Theory’ for mathematicians and engineers. His research expertise encompasses the adaptive control of nonlinear systems and linear differential-algebraic equations. In cooperation with Professor Ryan (Bath, UK), he developed the concept of funnel control. In addition, he regularly delivered lectures on philosophical topics and published several books on Baroque architecture and the oval.

Publications

Latest publications

Thomas Berger, Achim Ilchmann and Eugene P. Ryan: Some remarks on positive/negative feedback. Systems and Control Letters 211, article 106394, 2026
[IR-2025] Achim Ilchmann and Hole Rößler (Eds.): Das Oval der Bücher. Die Wolfenbütteler Bibliotheksrotunde (1705--1887). Wolfenbütteler Forschungen 182, Herzog August Bibliothek, Wolfenbüttel 2025
Achim Ilchmann and Angelo A. Mazzotti: Das Korb´sche Oval. Eine Rekonstruktion gemäß dem Barock. p. 61-75 in [IR-2025]
Achim Ilchmann: Das Oval -- eine Augenweide. Das Schöne im Korb´schen Oval. p. 125-134 in [IR-2025]
Achim Ilchmann and Hole Rößler: „aus lauter Circkelstücken zusammen gesetzt“. Materialien zur Wissensgeschichte des Ovals in der Frühen Neuzeit. p. 159-222 in [IR-2025]
Diederich Hinrichsen, Anthony J. Pritchard, Fritz Colonius, Tobias Damm, Achim Ilchmann, Birgit Jacob, Fabian R. Wirth: Mathematical Systems Theory II. Control, Observation, Realization, and Feedback. Springer-Verlag, Berlin 2026
Diederich Hinrichsen, Anthony J. Pritchard, Fritz Colonius, Tobias Damm, Achim Ilchmann, Birgit Jacob, Fabian R. Wirth: Mathematical Systems Theory III. Linear Quadratic Control and Adaptive Feedback. Springer-Verlag, Berlin 2026
Achim Ilchmann, Jonas Kirchhoff und Manuel Schaller: Port-Hamiltonian descriptor systems are generically controllable and stabilizable. Mathematics of Control, Signals, and Systems 37, 23-59, 2025
Thomas Berger, Achim Ilchmann and Eugene P. Ryan: Funnel control -- a survey. Annual Reviews in Control 2025
Thomas Hotz and Achim Ilchmann: Benedetti’s constructions of ovals. Historia Mathematica 2025
Achim Ilchmann: Das barocke Geheimnis des Bibliotheksstempels. p. 50-53 in 'SupraLibros' Mitteilungen der Gesellschaft Anna Amalia Bibliothek, Heft 30, Juni 2025
Fritz Barth and Achim Ilchmann: Ovale & Blicke. Dominikus Zimmermanns Wallfahrtskirche in Steinhausen. Edition Axel Menges, Stuttgart 2025

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Diederich Hinrichsen, Anthony J. Pritchard, Fritz Colonius, Tobias Damm, Achim Ilchmann, Birgit Jacob, Fabian R. Wirth
Mathematical Systems Theory II. Control, Observation, Realization, and Feedback.
Springer-Verlag, Berlin 2026
Diederich Hinrichsen, Anthony J. Pritchard, Fritz Colonius, Tobias Damm, Achim Ilchmann, Birgit Jacob, Fabian R. Wirth
Mathematical Systems Theory III. Linear Quadratic Control and Adaptive Feedback.
Springer-Verlag, Berlin 2026
Fritz Barth and Achim Ilchmann
Ovale & Blicke. Dominikus Zimmermanns Wallfahrtskirche in Steinhausen.
Edition Axel Menges, Stuttgart 2025
Achim Ilchmann and Hole Rößler (Eds.)
Das Oval der Bücher. Die Wolfenbütteler Bibliotheksrotunde (1705--1887).
Wolfenbütteler Forschungen 182, Herzog August Bibliothek, Wolfenbüttel 2025
Achim Ilchmann
Das Rokoko in der Herzogin Anna Amalia Bibliothek.
Harrassowitz Verlag, Wiesbaden 2023
Campbell, S., Ilchmann, A., Mehrmann, V., Reis, T. (Eds.)
Applications of Differential-Algebraic Equations: Examples and Benchmarks
Differential-Algebraic Equations Forum.
Berlin/Heidelberg: Springer-Verlag, 2019
doi:10.1007/978-3-030-03718-5
Achim Ilchmann
Die Baugeschichte eines Rokoko-Stadthauses
Erfurt: Ulenspiegel-Verlag, 2018
Inhaltsverzeichnis und Geleitwort
Rezension „Leipziger Internet Zeitung“
Achim Ilchmann
Das bürgerliche Stadthaus im Rokoko
Tübingen/Berlin: Ernst Wasmuth Verlag, 2018
Inhaltsverzeichnis
Rezension „Leipziger Internet Zeitung“
Achim Ilchmann
Mathematik und Gesellschaft. Zur Funktion der angewandten Mathematik
Leipzig: EAGLE-Verlag, 2016 [PDF]
Rezension „Leipziger Internet Zeitung“
Achim Ilchmann
Non-Identifier-Based High-Gain Adaptive Control
Lecture Notes in Control and Information Sciences 184.
London: Springer, 1993 [PDF]
Achim Ilchmann
Contributions To Time-Varying Linear Control Systems
Hamburg: Verlag an der Lottbek, 1989 [PDF]
Achim Ilchmann, Timo Reis (Eds.)
Surveys in Differential-Algebraic Equations IV
Differential-Algebraic Equations Forum.
Berlin/Heidelberg: Springer-Verlag, 2017
doi:10.1007/978-3-319-46618-7
Achim Ilchmann, Timo Reis (Eds.)
Surveys in Differential-Algebraic Equations III
Berlin/Heidelberg: Springer-Verlag, 2015
doi:10.1007/978-3-319-22428-2
Achim Ilchmann, Timo Reis (Eds.)
Surveys in Differential-Algebraic Equations II
Differential-Algebraic Equations Forum.
Berlin/Heidelberg: Springer-Verlag, 2014
doi:10.1007/978-3-319-11050-9
Achim Ilchmann, Timo Reis (Eds.)
Surveys in Differential-Algebraic Equations I
Differential-Algebraic Equations Forum.
Berlin/Heidelberg: Springer-Verlag, 2013
doi:10.1007/978-3-642-34928-7

A. Ilchmann, J. Kirchhoff
Relative genericity of controllablity and stabilizability for differential-algebraic systems
Mathematics of Control, Signals, and Systems 35: 45-76, 2023
A. Ilchmann, J. Kirchhoff
Differential-algebraic systems are generically controllable and stabilizable
Mathematics of Control, Signals, and Systems 33(3): 359-377, 2021
A. Ilchmann, J. Witschel, K. Worthmann
Model predictive control for singular differential-algebraic equations
Int. J. Control 95(8):1-19, 2021
A. Ilchmann, J. Witschel, K. Worthmann
Model predictive control for singular differential-algebraic equations
to appear in International Journal of Control, 2021 [PDF]
A. Ilchmann, J. Kirchhoff
Differential-algebraic systems are generically controllable and stabilizable,
Mathematics of Control, Signals, and Systems 33(3): 359-377, 2021
A. Ilchmann, L. Leben, J. Witschel, K. Worthmann
Optimal control of differential-algebraic equations from an ordinary differential equation perspective
Optimal Control, Applications and Methods, 40:351-366, 2019 [PDF]
A. Ilchmann, T. Reis
Outer transfer functions of differential-algebraic systems
ESAIM: Control, Opt. and Calculus of Variations 23(2) (2017) 391-425 [pdf]
Th. Berger, A. Ilchmann and T. Reis
Funnel control for nonlinear functional differential-algebraic systems
MTNS, Groningen pp. 46-53 (2014) [pdf]
Th. Berger, A. Ilchmann and T. Reis
Normal forms, high-gain and funnel control for linear differential-algebraic systems
pp. 127-164 in "Control and Optimization with Differential-Algebraic Constraints", Eds.: L. Biegler, S.L. Campbell, V. Mehrmann; SIAM, Philadelphia (2012) [pdf]
Th. Berger, A. Ilchmann and T. Reis
Zero dynamics and funnel control of linear differential-algebraic systems
Mathematics of Control, Signals and Systems 24(3) (2012) 219-263 [pdf]
Th. Berger and A. Ilchmann
On stability of time-varying linear differential-algebraic equations
Int. J. of Control 86(6) (2013) 1060–1076 [pdf]
Th. Berger and A. Ilchmann
On the standard canonical form of time-varying linear DAEs
Quarterly of Applied Mathematics 71 (2013) 69-87 [pdf]
Th. Berger, A. Ilchmann and St. Trenn
The quasi-Weierstraß form for regular matrix pencils
Linear Algebra and its Appl. 436 (2012) 4052-4069 [pdf]
A. Ilchmann and V. Mehrmann
A behavioural approach to time-varying linear systems, Part 2: Descriptor systems
SIAM J. of Control and Optimization 44 (2005) 1748-1765 [pdf]
A. Ilchmann and V. Mehrmann
A behavioural approach to time-varying linear systems, Part 1: General theory
SIAM J. of Control and Optimization 44 (2005) 1725-1747 [pdf]
A. Ilchmann
Algebraic theory of time-varying linear systems: a survey
in `Selected Plenaries, Milestones and Surveys' Eds.: P. Horacek, M. Simandl, P. Zitek; Prague, Czech Republic (2005) 312-318 [pdf]
M.d.R. De Pinho and A. Ilchmann
Weak maximum principle for optimal problems with mixed constraints
Nonlinear Analysis 48 (2002) 1179-1196 [pdf]
A. Ilchmann
Time-varying linear systems and invariants of system equivalence
Int. J. Control 42 (1985) 759-790 [pdf]
A. Ilchmann, I. Nürnberger and W. Schmale
Time-varying polynomial matrix systems
Int. J. Control 40 (1984) 329-362 [pdf]

Th. Berger, A. Ilchmann and F. Wirth
Zero dynamics and stabilization for analytic linear systems
Acta Applicandae Mathematicae 138(1) (2015) 17-57
B. D. O. Anderson, A. Ilchmann and F. R. Wirth
Stabilizability of linear time-varying systems
Systems and Control Letters 62(9) (2013) 747–755
Achim Ilchmann and Fabian Wirth
On Minimum Phase
at-Automatisierungstechnik 61(12) (2013) 805–817 [pdf]
A. Ilchmann and P.H.A. Ngoc
Stability and robust stability of positive Volterra systems
Int. J. Robust and Nonlinear Control 22(6) (2012) 604-629 [pdf]
Achim Ilchmann, Zhenqing Ke, Hartmut Logemann
Indirect sampled-data control with sampling period adaptation
Int. J. Control 84(2) (2011) 424-431 [pdf]
A. Ilchmann and Adrian T. Hill
Exponential stability of time-varying linear systems
IMA Journal of Numerical Analysis 31(3) (2011) 865-885
Th. Berger and A. Ilchmann
Zero dynamics of time-varying linear systems
Preprint 10-05 (2010)
M. French, A. Ilchmann and M. Mueller
Robust stabilization by linear output delay feedback
SIAM J. of Control and Optimization 48 (2009) 2533–2561 [pdf]
A. Ilchmann and P.H.A. Ngoc
On positivity and stability of linear time-varying Volterra equations
Positivity 13(4) (2009) 671-681
A. Ilchmann and M. Mueller
Time-varying linear systems: relative degree and normal form
IEEE Trans. Aut. Control 52 (2007) 840-851
H. Crauel, T. Damm and A. Ilchmann
Stabilization of linear systems by rotation
J. of Differential Equations 234 (2007) 412-438
A. Ilchmann, O. Sawodny and S. Trenn
Pneumatic cylinders: modelling and feedback force-control
Int. J. Control 79 (2006) 650-661 [pdf]
L. H. Duc, A. Ilchmann, S. Siegmund and P. Taraba
On stability of linear time-varying second-order differential equations
Quarterly of Appl. Maths. 64 (2006) 137-151
A. Ilchmann and C.J. Sangwin
Output feedback stabilisation by delays
Systems & Control Lett. 52 (2004) 233-245 [pdf]

A. Ilchmann and I.M.Y. Mareels
On stability radii of slowly time-varying systems
Advances in Mathematical Systems Theory, Eds.:F. Colonius, U. Helmke, D. Prätzel-Wolters, F. Wirth, Birkhäuser Verlag, Boston (2000) 55-75
A. Ilchmann and B. Werner
Characterization of the stability radius via bifurcation techniques
Applicable Analysis 52 (1994) 231-246
D. Hinrichsen, A. Ilchmann and A. J. Pritchard
A stability radius for time-varying linear systems
The Mathematics of Control Theory, Eds.: N. K. Nichols and D. H. Owens, Oxford University Press, Oxford (1992) 281-290
D. Hinrichsen , A. Ilchmann and A. J. Pritchard
Robustness of stability of time-varying linear systems
J. of Differential Equations 82 (1989) 219-250
A. Ilchmann and G. Kern
Stabilizability of systems with exponential dichotomy
Systems & Control Lett. 8 (1987) 211-220
A. Ilchmann, D. H. Owens and D. Prätzel-Wolters
Sufficient conditions for stability of linear time-varying systems
Systems & Control Lett. 9 (1987) 157-163

Thomas Berger, Achim Ilchmann, Eugene P. Ryan
Some remarks on positive/negative feedback
Systems and Control Letters 211, article 106394, 2026
T. Berger, A. Ilchmann, E. P. Ryan
Funnel control – a survey
Annual Reviews in Control 60, 2025
T. Berger, D. Dennstädt, A. Ilchmann, K. Worthmann
Funnel MPC for nonlinear systems with relative degree one
SIAM J. on Control and Opt. 60(6): 3358-3383, 2022 [PDF]
T. Berger, A. Ilchmann, E. P. Ryan
Funnel control of nonlinear systems
Mathematics of Control, Signals, and Systems 33:151--194, 2021 [PDF]
Th. Berger, A. Ilchmann and T. Reis
Funnel control for nonlinear functional differential-algebraic systems
MTNS Groningen, The Netherlands (2014) 46--53
A. Ilchmann, T. Selig, C. Trunk
The Byrnes-Isidori form for infinite-dimensional systems
SIAM J. Control and Opt. 54(3):1504-1534, (2016)
Th. Berger, A. Ilchmann and T. Reis
Normal forms, high-gain and funnel control for linear differential-algebraic systems
pp. 127-164 in "Control and Optimization with Differential-Algebraic Constraints", Eds.: L. Biegler, S.L. Campbell, V. Mehrmann; SIAM, Philadelphia (2012)
Th. Berger, A. Ilchmann and T. Reis
Zero dynamics and funnel control of linear differential-algebraic systems
Mathematics of Control, Signals and Systems 24(3) (2012) 219-263
A. Ilchmann
Decentralized tracking of interconnected systems
in: Knut Hüper and Jochen Trumpf (eds.), Mathematical System Theory - Festschrift in Honor of Uwe Helmke on the Occasion of his Sixtieth Birthday, CreateSpace (2013) 229-245
C. Hackl, N. Hopfe, A. Ilchmann, M. Mueller and S. Trenn
Funnel Control for systems with relative degree two
SIAM J. of Control and Optimization 51(2):(2013) 965–995
A. Ilchmann, H. Logemann and E. P. Ryan
Tracking with prescribed transient performance for hysteretic systems
SIAM J. of Control and Optimization 48(7):(2010) 4731-4752
N. Hopfe, A. Ilchmann and E. P. Ryan
Funnel control with saturation: nonlinear SISO systems
IEEE Trans. Automatic Control 55(9):(2010) 2177-2182
N. Hopfe, A. Ilchmann and E. P. Ryan
Funnel control with saturation: linear MIMO systems
IEEE Trans. Automatic Control 55(2): (2010) 532-538
A. Ilchmann and M. Mueller
Robustness of funnel control in the gap metric
SIAM J. of Control and Optimization 47(5): (2009) 2724-2744
A. Ilchmann and E. P. Ryan
Performance funnels and tracking control
Int. J. of Control 82(10): (2009) 1828-1840
A. Ilchmann and H. Schuster
PI-funnel control for two mass systems
IEEE Trans. Automatic Control 54 (2009) 918-923
A. Ilchmann and E. P. Ryan
High-gain control without identification: a survey
GAMM-Mitteilungen 31 (2008) 115-125
A. Ilchmann, E. P. Ryan and P. Townsend
Tracking with prescribed transient behaviour for nonlinear systems of known relative degree
SIAM J. of Control and Optimization 46 (2007) 210-230
A. Ilchmann and E. P. Ryan
Asymptotic tracking with prescribed transient behaviour for linear systems
Int. J. Control 79 (2006) 910-917
A. Ilchmann, E. P. Ryan and P. Townsend
Tracking control with prescribed transient behaviour for systems of known relative degree
Systems & Control Lett. 55 (2006) 396-406
A. Ilchmann, E.P. Ryan and S. Trenn
Tracking control: performance funnels and prescribed transient behaviour
Systems & Control Lett. 54 (2005) 655-670
A. Ilchmann and S. Trenn
Input constrained funnel control with applications to chemical reactor models
Systems & Control Lett. 53 (2004) 361-375
A. Ilchmann, E.P. Ryan and C.J. Sangwin
Tracking with prescribed transient behaviour
ESAIM: Control, Optimisation and Calculus of Variations 7 (2002) 471-493
A. Ilchmann
Non-identifier-based adaptive control of dynamical systems: a survey
IMA J. of Math. Control and Inf. 8 (1991) 321-366

M. French, A. Ilchmann and E. P. Ryan
Robustness in the graph topology of a common adaptive controller
SIAM J. of Control and Optimization 45 (2006) 1736-1757
A. Ilchmann, S. Townley and M. Thuto
Adaptive sampled-data tracking for input constrained exothermic chemical reaction models
Systems & Control Lett. 54 (2005) 1149-1161
A. Ilchmann and E.P. Ryan
On tracking and disturbance rejection by adaptive control
Systems & Control Lett. 52 (2004) 137-147
A. Ilchmann and E.P. Ryan
On gain adaptation in adaptive control
IEEE Trans. Aut. Control 48 (2003) 895-899
A. Ilchmann and A. Isidori
Adaptive dynamic output feedback stabilisation of nonlinear systems
Asian Journal of Control 4 (2002) 1-9
P. Georgieva, A. Ilchmann and M.-F. Weirig
Modelling and adaptive control of aerobic continuous stirred tank reactors
European J. of Control 7 (2001) 476-491
I.M.Y.Mareels, S. Van Gils, J.W. Polderman and A. Ilchmann
Asymptotic dynamics in adaptive gain control
Advances in Control, Highlights of ECC '99, Ed.: P.M. Frank, Springer-Verlag, London (1999) 29-63
A. Ilchmann and S. Townley
Adaptive sampling control of high-gain stabilizable systems
IEEE Trans. Autom. Control 44 (1999) 1961-1966
A. Ilchmann
Universal adaptive control of nonlinear systems
Dynamics and Control 7 (1997) 199-213
A. Ilchmann
Adaptive stabilization
EncyclopaediaofMathematics, First Supplement, Managing Ed.:M.Hazewinkel,KluwerAcademic Publishers, Dordrecht, Boston (1997) 28-29 [pdf]
H. Logemann and A. Ilchmann
An adaptive servomechanism for a class of infinite-dimensional systems
SIAM J. on Control and Opt. 32 (1994) 917-936
A. Ilchmann
Adaptive controllers and root-loci of minimum phase systems
Dynamics and Control 4 (1994) 203-226
A. Ilchmann
Non-Identifier-Based High-Gain Adaptive Control
Lecture Notes in Control and Information Sciences 189, Springer-Verlag, London (1993)
A. Ilchmann and S. Townley
Simple adaptive stabilization of high-gain stabilizable systems
Systems & Control Lett. 20 (1993) 189-198
A. Ilchmann and D.H. Owens
Adaptive exponential tracking for nonlinearly perturbed minimum phase systems
Control-Theory and Advanced Technology 9 (1993) 353-379
A. Ilchmann and H. Logemann
High-gain adaptive tabilization of multivariable linear systems - revisited
Systems & Control Lett. 18 (1992) 355-364
A. Ilchmann and D. H. Owens
Exponential stabilization using non-differential gain adaptation
IMA J. of Math. Control and Inf. 7 (1991) 339-349
A. Ilchmann and D. H. Owens
Threshold switching functions in high-gain adaptive control
IMA J. of Math. Control and Inf. 8 (1991) 409-429
A. Ilchmann
Robust adaptive stabilization of discrete first order systems
Automatica 27 (1991) 829-835
A. Ilchmann and D. H. Owens
Adaptive stabilization with exponential decay
Systems & Control Lett. 14 (1990) 437-443
D. Prätzel-Wolters, D. H. Owens and A. Ilchmann
Robust adaptive stabilization by high gain and switching
Int. J. Control 49 (1989) 1861-1868
A. Ilchmann, D. H. Owens and D. Prätzel-Wolters
High gain robust adaptive controllers for multivariable systems
Systems & Control Lett. 8 (1987) 397-404
D. H. Owens, D. Prätzel-Wolters and A. Ilchmann
Positive real structure and high gain adaptive stabilization
IMA J. of Math. Control and Inf. 4 (1987) 167-181

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Prof. Dr. Achim Ilchmann