Differential-algebraic systems are generically controllable and stabilizable. - In: Mathematics of control, signals, and systems : MCSS.. - London : Springer, ISSN 1435-568X, Bd. 33 (2021), 3, S. 359-377
We investigate genericity of various controllability and stabilizability concepts of linear, time-invariant differential-algebraic systems. Based on well-known algebraic characterizations of these concepts (see the survey article by Berger and Reis (in: Ilchmann A, Reis T (eds) Surveys in differential-algebraic equations I, Differential-Algebraic Equations Forum, Springer, Berlin, pp 1-61. https://doi.org/10.1007/978-3-642-34928-7_1)), we use tools from algebraic geometry to characterize genericity of controllability and stabilizability in terms of matrix formats.
Funnel control of nonlinear systems. - In: Mathematics of control, signals, and systems : MCSS.. - London : Springer, ISSN 1435-568X, Bd. 33 (2021), 1, S. 151-194
Tracking of reference signals is addressed in the context of a class of nonlinear controlled systems modelled by r-th-order functional differential equations, encompassing inter alia systems with unknown "control direction" and dead-zone input effects. A control structure is developed which ensures that, for every member of the underlying system class and every admissible reference signal, the tracking error evolves in a prescribed funnel chosen to reflect transient and asymptotic accuracy objectives. Two fundamental properties underpin the system class: bounded-input bounded-output stable internal dynamics, and a high-gain property (an antecedent of which is the concept of sign-definite high-frequency gain in the context of linear systems).
Applications of differential-algebraic equations: examples and benchmarks. - Cham : Springer, 2019. - vii, 320 Seiten. . - (Differential-algebraic equations forum) ISBN 3-030-03717-7
Optimal control of differential-algebraic equations from an ordinary differential equation perspective. - In: Optimal control, applications and methods. - New York, NY [u.a.] : Wiley, ISSN 1099-1514, Bd. 40 (2019), 2, S. 351-366
The gap distance to the set of singular matrix pencils. - In: Linear algebra and its applications : LAA.. - New York, NY : American Elsevier Publ., Bd. 564 (2019), S. 28-57
Die Baugeschichte eines Rokoko-Stadthauses. - Erfurt : Ulenspiegel, 2018. - 253 Seiten. ISBN 978-3-932655-56-2
Model predictive control for linear DAEs without terminal constraints and costs. - In: IFAC-PapersOnLine. - Frankfurt : Elsevier, ISSN 2405-8963, Bd. 51 (2018), 20, S. 116-121
Model predictive control for linear differential-algebraic equations. - In: IFAC-PapersOnLine. - Frankfurt : Elsevier, ISSN 2405-8963, Bd. 51 (2018), 20, S. 98-103
Finite rank perturbations of linear relations and singular matrix pencils. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2018. - 1 Online-Ressource (25 Seiten). . - (Preprint. - M18,08)
We elaborate on the deviation of the Jordan structures of two linear relations that are finite-dimensional perturbations of each other. We compare the number of Jordan chains of length at least n corresponding to some eigenvalue to each other. In the operator case, it was recently proved that the difference of these numbers is independent of n and is at most the defect between the operators. One of the main results of this paper shows that in the case of linear relations this number has to be multiplied by n+1 and that this bound is sharp. The reason for this behaviour is the existence of singular chains. We apply our results to one-dimensional perturbations of singular and regular matrix pencils. This is done by representing matrix pencils via linear relations. This technique allows for both proving known results for regular pencils as well as new results for singular ones.
Das bürgerliche Stadthaus im Rokoko. - Tübingen : Wasmuth, 2018. - 255 Seiten. ISBN 3-8030-0833-6