Submitted

@unpublished{TrenSutr24pp,

title = {Model reduction of singular switched systems in discrete time},

author = {Stephan Trenn and Sutrisno and Do Duc Thuan and Phi Ha},

url = {https://stephantrenn.net/wp-content/uploads/2025/01/Preprint-TSTP241108.pdf, Preprint},

year  = {2024},

date = {2024-11-08},

urldate = {2024-11-08},

abstract = {Based on our recently established solution characterization of switched singular descriptor systems in discrete time, we propose a time-varying balanced truncation method. For that we consider the switched system on a finite time interval and define corresponding time-varying reachability and observability Gramians. We then show that these capture essential quantitative information about reachable and observable state directions. Based on these Gramians we formulate a time-varying balanced truncation method resulting in a fully-time varying linear system with possible varying state dimensions. We illustrate this method with a small dynamic Leontief model, where we can reduce the size to one third without altering the input-output behavior significantly. We also show that the method is suitable for a medium size random descriptor system (100 x100) resulting in a time-varying system of less then a tenth of the size where the outputs of the original and reduced system are indistinguishable.},

note = {submitted},

keywords = {},

pubstate = {published},

tppubtype = {unpublished}

}

@unpublished{WijnTren24pp,

title = {Impulse-free linear quadratic optimal control of switched differential algebraic equations},

author = {Paul Wijnbergen and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2024/07/Preprint-WT240512.pdf, Preprint},

year  = {2024},

date = {2024-05-12},

urldate = {2024-05-12},

abstract = {In this paper the finite horizon linear quadratic regulator (LQR) problem for switched linear differential algebraic equations is studied. It is shown that for switched DAEs with a switching signal that induces locally finitely many switches, the problem can be solved by recursively solving several LQR problems for non-switched DAE. First, it is shown how to solve the non-switched problems for index-1 DAEs followed by an extension of the results to higher index DAEs. The resulting optimal control can be computed based on the solution of a Riccati differential equation expressed in terms of the differential system matrices. The paper concludes with the extension of the results to the LQR problem for general switched DAEs.},

note = {provisionally accepted in "Communications in Optimization Theory"},

keywords = {},

pubstate = {published},

tppubtype = {unpublished}

}

@unpublished{YinJaya23ppa,

title = {Contraction analysis of time-varying DAE systems via auxiliary ODE systems},

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

url = {https://stephantrenn.net/wp-content/uploads/2023/12/Preprint-YJT230920.pdf, Preprint},

year  = {2023},

date = {2023-09-20},

urldate = {2023-09-20},

note = {conditionally accepted at TAC},

keywords = {},

pubstate = {published},

tppubtype = {unpublished}

}