Stephan Trenn

@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{MostTren22a,

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/2021/09/Preprint-MTV210921.pdf, Preprint},

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

year  = {2022},

date = {2022-02-01},

urldate = {2022-02-01},

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}

}

@article{BergIlch22,

title = {Quasi feedback forms for differential-algebraic systems},

author = {Thomas Berger and Achim Ilchmann and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2023/01/BergIlch22.pdf, Paper

https://arxiv.org/abs/2102.12713, arXiv:2102.12713},

doi = {10.1093/imamci/dnab030},

year  = {2022},

date = {2022-06-01},

urldate = {2022-06-01},

journal = {IMA Journal of Mathematical Control and Information},

volume = {39},

issue = {2},

pages = {533-563},

abstract = {We investigate feedback forms for linear time-invariant systems described by differential-algebraic equations. Feedback forms are representatives of certain equivalence classes. For example state space transformations, invertible transformations from the left, and proportional state feedback constitute an equivalence relation. The representative of such an equivalence class, which we call proportional feedback form for the above example, allows to read off relevant system theoretic properties. Our main contribution is to derive a quasi proportional feedback form. This form is advantageous since it provides some geometric insight and is simple to compute, but still allows to read off the relevant structural properties of the control system. We also derive a quasi proportional and derivative feedback form. Similar advantages hold.},

note = {open access, published online October 2021},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{BorsKoco20,

title = {A distributional solution framework for linear hyperbolic PDEs coupled to switched DAEs},

author = {Raul Borsche and Damla Kocoglu and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2020/11/23-MCSS2020.pdf, Paper},

doi = {10.1007/s00498-020-00267-7},

year  = {2020},

date = {2020-11-18},

urldate = {2020-11-18},

journal = {Mathematics of Control, Signals, and Systems (MCSS)},

volume = {32},

pages = {455-487},

abstract = {A distributional solution framework is developed for systems consisting of linear hyperbolic partial differential equations (PDEs) and switched differential-algebraic equations (DAEs) which are coupled via boundary conditions. The unique solvability is then characterize in terms of a switched delay DAE. The theory is illustrated with an example of electric power lines modeled by the telegraph equations which are coupled via a switching transformer where simulations confirm the predicted impulsive solutions.},

note = {Open Access},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{IervTren21,

title = {Asymptotic stability of piecewise affine systems with Filippov solutions via discontinuous piecewise Lyapunov functions},

author = {Raffaele Iervolino and Stephan Trenn and Francesco Vasca},

url = {https://stephantrenn.net/wp-content/uploads/2020/02/Preprint-ITV200204.pdf, Preprint},

doi = {10.1109/TAC.2020.2996597},

year  = {2021},

date = {2021-04-01},

urldate = {2021-04-01},

journal = {IEEE Transactions on Automatic Control},

volume = {66},

number = {4},

pages = {1513-1528},

abstract = {Asymptotic stability of continuous-time piecewise affine systems defined over a polyhedral partition of the state space, with possible discontinuous vector field on the boundaries, is considered. In the first part of the paper the feasible Filippov solution concept is introduced by characterizing single-mode Caratheodory, sliding mode and forward Zeno behaviors. Then, a global asymptotic stability result through a (possibly discontinuous) piecewise Lyapunov function is presented. The sufficient conditions are based on pointwise classifications of the trajectories which allow the identification of crossing, unreachable and Caratheodory boundaries. It is shown that the sign and jump conditions of the stability theorem can be expressed in terms of linear matrix inequalities by particularizing to piecewise quadratic Lyapunov functions and using the cone-copositivity approach. Several examples illustrate the theoretical arguments and the effectiveness of the stability result.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{AnhLinh20,

title = {Stability analysis for switched discrete-time linear singular systems},

author = {Pham Ky Anh and Pham Thi Linh and Do Duc Thuan and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2020/02/Preprint-ALTT200515.pdf, Preprint},

doi = {10.1016/j.automatica.2020.109100},

year  = {2020},

date = {2020-09-01},

urldate = {2020-09-01},

journal = {Automatica},

volume = {119},

number = {109100},

abstract = {The stability of arbitrarily switched discrete-time linear singular (SDLS) systems is studied. Our analysis builds on the recently introduced one-step-map for SDLS systems of index-1. We first provide a sufficient stability conditions in terms of Lyapunov functions. Furthermore, we generalize the notion of joint spectral radius of a finite set of matrix pairs, which allows us to fully characterize exponential stability.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}