Geodesic
Controllability, observability, realizability, and stability of dynamic linear systems
Electronic Journal of Differential Equations, Tome 2009 (2009).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time scales. The approach here is based on generalized Laplace transform methods (e.g. shifts and convolution) from the recent work [13]. We study controllability in terms of the controllability Gramian and various rank conditions (including Kalman's) in both the time invariant and time varying settings and compare the results. We explore observability in terms of both Gramian and rank conditions and establish related realizability results. We conclude by applying this systems theory to connect exponential and BIBO stability problems in this general setting. Numerous examples are included to show the utility of these results.
Classification : 93B05, 93B07, 93B20, 93B55, 93D99
Keywords: systems theory, time scale, controllability, observability, realizability, Gramian, exponential stability, BIBO stability, generalized Laplace transform, convolution 
@article{EJDE_2009__2009__a185,
     author = {Davis, John M. and Gravagne, Ian A. and Jackson, Billy J. and Marks II, Robert J.},
     title = {Controllability, observability, realizability, and stability of dynamic linear systems},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2009},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a185/}
}
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Davis, John M.; Gravagne, Ian A.; Jackson, Billy J.; Marks II, Robert J. Controllability, observability, realizability, and stability of dynamic linear systems. Electronic Journal of Differential Equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a185/