%0 Journal Article %1 Yip1981Solvability %A Yip, E. %A Sincovec, R. %D 1981 %I IEEE %J IEEE Transactions on Automatic Control %K 93b11-system-structure-simplification 34a09-implicit-odes-daes %N 3 %P 702--707 %R 10.1109/tac.1981.1102699 %T Solvability, Controllability, and Observability of Continuous Descriptor Systems %U http://dx.doi.org/10.1109/tac.1981.1102699 %V 26 %X In this paper, we investigate the properties of the continuous descriptor system \$Ex(t)=Ax(t)+Bu(t), 0tb where E\$, \$A\$,and \$B\$ are complex and possibly singular matrices andu(t)is a complex function differentiable sufficiently many times. The traditional approach to such systems is to separate the state equations from the algebraic equations. However, such algorithms usually destroy the natural, physically-based sparsity and structure of the original system. Therefore, we consider descriptor systems in their original form. Such systems possess numerous properties not shared by the well-known state variable systems. First, we relate classical theories of matrix pencils to the solvability of descriptor systems. Then we extend the concepts of reachability, controllability, and observability of state variable systems to descriptor systems, and describe the set of reachable states for descriptor systems.

@article{Yip1981Solvability, abstract = {In this paper, we investigate the properties of the continuous descriptor system \$E\dot{x}(t)=Ax(t)+Bu(t), 0\leq t\leq b\text{ where }E\$, \$A\$,and \$B\$ are complex and possibly singular matrices andu(t)is a complex function differentiable sufficiently many times. The traditional approach to such systems is to separate the state equations from the algebraic equations. However, such algorithms usually destroy the natural, physically-based sparsity and structure of the original system. Therefore, we consider descriptor systems in their original form. Such systems possess numerous properties not shared by the well-known state variable systems. First, we relate classical theories of matrix pencils to the solvability of descriptor systems. Then we extend the concepts of reachability, controllability, and observability of state variable systems to descriptor systems, and describe the set of reachable states for descriptor systems.}, added-at = {2019-03-01T00:11:50.000+0100}, author = {Yip, E. and Sincovec, R.}, biburl = {https://www.bibsonomy.org/bibtex/26065d0924bc608df5ec88df92994287a/gdmcbain}, citeulike-article-id = {11389450}, citeulike-attachment-1 = {yip_81_solvability_836742.pdf; /pdf/user/gdmcbain/article/11389450/836742/yip_81_solvability_836742.pdf; b8d70252381c2a147c9c1843ee2ec7f175767dc1}, citeulike-linkout-0 = {http://dx.doi.org/10.1109/tac.1981.1102699}, citeulike-linkout-1 = {http://ieeexplore.ieee.org/xpls/abs\_all.jsp?arnumber=1102699}, comment = {(private-note)I found this looking for Sincovec et al (1979), as cited by Petzold (1982). ---=note-separator=--- (private-note)circulated by mshepit 2012-10-05}, doi = {10.1109/tac.1981.1102699}, file = {yip_81_solvability_836742.pdf}, institution = {Boeing Computer Services Company, Tukwila, WA, USA}, interhash = {28cf6b62948bd5843c572f1134ecfe5b}, intrahash = {6065d0924bc608df5ec88df92994287a}, issn = {0018-9286}, journal = {IEEE Transactions on Automatic Control}, keywords = {93b11-system-structure-simplification 34a09-implicit-odes-daes}, month = jun, number = 3, pages = {702--707}, posted-at = {2012-10-04 15:15:34}, priority = {0}, publisher = {IEEE}, timestamp = {2022-05-20T04:25:34.000+0200}, title = {{Solvability, Controllability, and Observability of Continuous Descriptor Systems}}, url = {http://dx.doi.org/10.1109/tac.1981.1102699}, volume = 26, year = 1981 }