Author: stephan

@article{HossTren24,

title = {Midpoint based balanced truncation for switched linear systems with known switching signal},

author = {Sumon Hossain and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2023/05/Preprint-HT230508.pdf, Preprint},

doi = {10.1109/TAC.2023.3269721},

year  = {2024},

date = {2024-01-01},

urldate = {2024-01-01},

journal = {IEEE Transactions on Automatic Control},

volume = {69},

number = {1},

abstract = {We propose a novel model reduction approach for switched linear systems with known switching signal. The class of considered systems encompasses switched systems with mode-dependent state-dimension as well as impulsive systems. Our method is based on a suitable definition of (time-varying) reachability and observability Gramians and we show that these Gramians satisfy precise interpretations in terms of input and output energy. Based on balancing the midpoint Gramians, we propose a piecewise-constant projection based model reduction resulting in a switched linear system of smaller size.},

note = {2023 early access},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{ChenTren21d,

title = {Normal forms and internal regularization of nonlinear differential-algebraic control systems},

author = {Yahao Chen and Stephan Trenn and Witold Respondek},

url = {https://stephantrenn.net/wp-content/uploads/2021/06/ChenTren21d.pdf, Paper},

doi = {10.1002/rnc.5623},

year  = {2021},

date = {2021-04-13},

urldate = {2021-04-13},

journal = {International Journal of Robust and Nonlinear Control},

volume = {2021},

number = {31},

pages = {6562-6584},

abstract = {In this paper, we propose two normal forms for nonlinear differential-algebraic control systems (DACSs) under external feedback equivalence, using a notion called maximal controlled invariant submanifold. The two normal forms simplify the system structures and facilitate understanding the various roles of variables for nonlinear DACSs. Moreover, we study when a given nonlinear DACS is internally regularizable, i.e., when there exists a state feedback transforming the DACS into a differential-algebraic equation (DAE) with internal regularity, the latter notion is closely related to the existence and uniqueness of solutions of DAEs. We also revise a commonly used method in DAE solution theory, called the geometric reduction method. We apply this method to DACSs and formulate it as an algorithm, which is used to construct maximal controlled invariant submanifolds and to find internal regularization feedbacks. Two examples of mechanical systems are used to illustrate the proposed normal forms and to show how to internally regularize DACSs.},

note = {open access},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{HossTren23a,

title = {Reduced realization for switched linear systems with known mode sequence},

author = {Sumon Hossain and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2023/03/Preprint-HT230322.pdf, Preprint

https://doi.org/10.5281/zenodo.6410136, Matlab sources},

doi = {10.1016/j.automatica.2023.111065},

year  = {2023},

date = {2023-03-22},

urldate = {2023-03-22},

journal = {Automatica},

volume = {154},

number = {111065},

pages = {1-9},

abstract = {We consider switched linear systems with mode-dependent state-dimensions and/or state jumps and propose a method to obtain a switched system of reduced size with identical input-output behavior. Our approach is based in considering time-dependent reachability and unobservability spaces as well as suitable extended reachability and restricted unobservability spaces together with the notion of a weak Kalman decomposition. A key feature of our approach is that only the mode sequence of the switching signal needs to be known and not the exact switching times. However, the size of a minimal realization will in general depend on the mode durations, hence it cannot be expected that our method always leads to minimal realization. Nevertheless, we show that our method is optimal in the sense that a repeated application doesn’t lead to a further reduction and we also highlight a practically relevant special case, where minimality is achieved.},

note = {open access},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{YinJaya23,

title = {On contraction analysis of switched systems with mixed contracting-noncontracting modes via mode-dependent average dwell time},

author = {Hao Yin and Bayu Jayawardhana and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2022/04/Preprint-YJT221110.pdf, Preprint},

doi = {10.1109/TAC.2023.3237492},

year  = {2023},

date = {2023-01-16},

urldate = {2022-11-10},

journal = {IEEE Transactions on Automatic Control},

abstract = {This paper studies contraction analysis of switched systems that are composed of a mixture of contracting and non- contracting modes. The first result pertains to the equivalence of the contraction of a switched system and the uniform global ex- ponential stability of its variational system. Based on this equiva- lence property, sufficient conditions for a mode-dependent average dwell/leave-time based switching law to be contractive are estab- lished. Correspondingly, LMI conditions are derived that allow for numerical validation of contraction property of nonlinear switched systems, which include those with all non-contracting modes.},

note = {early access},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{ChenTren22a,

title = {Impulse-free jump solutions of nonlinear differential-algebraic equations},

author = {Yahao Chen and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2022/03/Preprint-CT220312.pdf, Preprint},

doi = {10.1016/j.nahs.2022.101238},

year  = {2022},

date = {2022-11-01},

urldate = {2022-11-01},

journal = {Nonlinear Analysis: Hybrid Systems},

volume = {46},

number = {101238},

pages = {1-17},

abstract = {In this paper, we propose a novel notion called impulse-free jump solution for nonlinear differential-algebraic equations (DAEs) of the form E(x)x' = F(x) with inconsistent initial values. The term “impulse-free” means that there are no Dirac impulses caused by jumps from inconsistent initial values, i.e., the directions of jumps stay in ker E(x). We find that the existence and uniqueness of impulse-free jumps are closely related to the notion of geometric index-1 and the involutivity of the distribution defined by ker E(x). Moreover, a singular perturbed system approximation is proposed for nonlinear DAEs; we show that solutions of the perturbed system approximate both impulse-free jump solutions and C1-solutions of nonlinear DAEs. Finally, we show by some examples that our results of impulse-free jumps are useful for the problems like consistent initializations of nonlinear DAEs and transient behavior simulations of electric circuits.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{LeeTren22,

title = {Synchronization with prescribed transient behavior: Heterogeneous multi-agent systems under funnel coupling},

author = {Jin Gyu Lee and Stephan Trenn and Hyungbo Shim},

url = {https://stephantrenn.net/wp-content/uploads/2022/08/LeeTren22.pdf, Paper

https://arxiv.org/abs/2012.14580, Extended ArXiv-version},

doi = {10.1016/j.automatica.2022.110276},

year  = {2022},

date = {2022-07-01},

urldate = {2022-07-01},

journal = {Automatica},

volume = {141},

number = {110276},

pages = {13},

abstract = {In this paper, we introduce a nonlinear time-varying coupling law, which can be designed in a fully decentralized manner and achieves approximate synchronization with arbitrary precision, under only mild assumptions on the individual vector fields and the underlying (undirected) graph structure. The proposed coupling law is motivated by the so-called funnel control method studied in adaptive control under the observation that arbitrary precision synchronization can be achieved for heterogeneous multi-agent systems by a high-gain coupling; consequently we call our novel synchronization method ‘(node-wise) funnel coupling.’ By adjusting the conventional proof technique in the funnel control study, we are even able to obtain asymptotic synchronization with the same funnel coupling law. Moreover, the emergent collective behavior that arises for a heterogeneous multi-agent system when enforcing arbitrary precision synchronization by the proposed funnel coupling law, is analyzed in this paper. In particular, we introduce a single scalar dynamics called ‘emergent dynamics’ which describes the emergent synchronized behavior of the multi-agent system under funnel coupling. Characterization of the emergent dynamics is important because, for instance, one can design the emergent dynamics first such that the solution trajectory behaves as desired, and then, provide a design guideline to each agent so that the constructed vector fields yield the desired emergent dynamics. We illustrate this idea via the example of a distributed median solver based on funnel coupling.},

note = {open access},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{MostTren22,

title = {A smooth model for periodically switched descriptor systems},

author = {Elisa Mostacciuolo and Stephan Trenn and Francesco Vasca},

url = {https://stephantrenn.net/wp-content/uploads/2021/04/Preprint-MTV210921.pdf, Preprint},

doi = {10.1016/j.automatica.2021.110082},

year  = {2022},

date = {2022-02-01},

urldate = {2021-09-21},

journal = {Automatica},

volume = {136},

number = {110082},

pages = {1-8},

abstract = {Switched descriptor systems characterized by a repetitive finite sequence of modes can exhibit state discontinuities at the switching time instants. The amplitudes of these discontinuities depend on the consistency projectors of the modes. A switched ordinary differential equations model whose continuous state evolution approximates the state of the original system is proposed. Sufficient conditions based on linear matrix inequalities on the modes projectors ensure that the approximation error is of linear order of the switching period. The theoretical findings are applied to a switched capacitor circuit and numerical results illustrate the practical usefulness of the proposed model.},

note = {open access},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Tren21,

title = {Distributional restriction impossible to define},

author = {Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2020/09/Preprint-Tre200901.pdf, Preprint},

doi = {10.1016/j.exco.2021.100023},

year  = {2021},

date = {2021-11-30},

urldate = {2021-11-30},

journal = {Examples and Counterexamples},

volume = {1},

number = {100023},

pages = {1-4},

abstract = {A counterexample is presented showing that it is not possible to define a restriction for distributions.},

note = {open access},

keywords = {},

pubstate = {published},

tppubtype = {article}

}