Publications

@unpublished{HossTren22ppc,

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/2022/05/Preprint-HT220422.pdf, Preprint},

year  = {2022},

date = {2022-04-22},

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 = {submitted},

keywords = {controllability, model-reduction, observability, switched-systems},

pubstate = {published},

tppubtype = {unpublished}

}

@unpublished{HossTren22ppb,

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

author = {Sumon Hossain and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2022/05/Preprint-HT220413.pdf, Preprint

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

year  = {2022},

date = {2022-04-13},

urldate = {2022-04-13},

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 = {submitted},

keywords = {controllability, model-reduction, observability, switched-systems},

pubstate = {published},

tppubtype = {unpublished}

}

@unpublished{HossTren21pp,

title = {Reduced realization of switched linear systems with known switching sequence},

author = {Sumon Hossain and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2021/10/Preprint-HT211016.pdf, Preprint},

year  = {2021},

date = {2021-10-16},

abstract = {We propose a novel reduction approach for switched linear systems with a fixed mode sequence based on subspaces related to the (time-varying) reachable and unobservable spaces. These subspaces are defined in such a way that they can be used to construct a switched weak Kalman decomposition, which is then in turn used to define a reduced switched linear system with an identical input-output behavior. The proposed method is illustrated with a low dimensional academic example.},

note = {submitted},

keywords = {controllability, model-reduction, observability, switched-systems},

pubstate = {published},

tppubtype = {unpublished}

}