Together with my PhD-students we have prepared the following two submission to the IFAC World Congress 2020 to be held in Berlin next year:
Hossain, Sumon; Trenn, Stephan A time-varying Gramian based model reduction approach for Linear Switched Systems Unpublished 2019, (submitted for publication). @unpublished{HossTren19pp, title = {A time-varying Gramian based model reduction approach for Linear Switched Systems}, author = {Sumon Hossain and Stephan Trenn}, url = {https://stephantrenn.net/wp-content/uploads/2019/12/Preprint-HT191118.pdf, Preprint}, year = {2019}, date = {2019-11-18}, abstract = {Switched system can be considered as a special class of piecewise constantly time- varying systems. In this paper, a model reduction approach is proposed for piecewise constantly switched systems, based on balancing based model order reduction (MOR) method for linear time-varying systems. Time-varying controllability and observability Gramians are computed in finite time interval and then developed balancing theory for the linear time-varying systems. A low dimensional approximate system is computed by applying projection based balanced truncation (BT) method. Finally, the proposed approach is illustrated numerically.}, note = {submitted for publication}, keywords = {}, pubstate = {published}, tppubtype = {unpublished} } Switched system can be considered as a special class of piecewise constantly time- varying systems. In this paper, a model reduction approach is proposed for piecewise constantly switched systems, based on balancing based model order reduction (MOR) method for linear time-varying systems. Time-varying controllability and observability Gramians are computed in finite time interval and then developed balancing theory for the linear time-varying systems. A low dimensional approximate system is computed by applying projection based balanced truncation (BT) method. Finally, the proposed approach is illustrated numerically. |
Wijnbergen, Paul; Jeeninga, Mark; Trenn, Stephan On stabilizability of switched Differential Algebraic Equations Unpublished 2019, (submitted for publication). @unpublished{WijnJeen19pp, title = {On stabilizability of switched Differential Algebraic Equations}, author = {Paul Wijnbergen and Mark Jeeninga and Stephan Trenn}, url = {https://stephantrenn.net/wp-content/uploads/2019/12/Preprint-WJT191118.pdf, Preprint}, year = {2019}, date = {2019-11-18}, abstract = {This paper considers stabilizability of switched differential algebraic equations (DAEs). We first introduce the notion of interval stabilizability and show that under a certain uniformity assumption, stabilizability can be concluded from interval stabilizability. A geometric approach is taken to find necessary and sufficient conditions for interval stabilizability. Then the analysis is extended resulting in a characterization of controllability.}, note = {submitted for publication}, keywords = {}, pubstate = {published}, tppubtype = {unpublished} } This paper considers stabilizability of switched differential algebraic equations (DAEs). We first introduce the notion of interval stabilizability and show that under a certain uniformity assumption, stabilizability can be concluded from interval stabilizability. A geometric approach is taken to find necessary and sufficient conditions for interval stabilizability. Then the analysis is extended resulting in a characterization of controllability. |