Componentwise stability of the singular discrete time system using the methodology of the Drazin inverse

Authors:
Habiba Mejhed;Nour El Houda Mejhed;Abdlaziz Hmamed
Affiliations:
-;Département Génie Informatique, Ecole Nationale des sciences appliquées de Fès., Université Sidi Mohammed Ben Abdallah, Fès, Morocco;LESSI Département de physique, Faculté des sciences, Université Sidi Mohammed Ben Abdallah, Fès, Morocco
Venue:
WSEAS Transactions on Systems and Control
Year:
2009

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Abstract

The asymptotic (exponential) stability in the sense of componentwise approach is considered for one and two dimensional linear discrete-time singular systems. The two dimensional system is described by Fornasini-Marchesini model. The main motivation for these results is the need, particularly felt in the evaluation in a more detailed manner of the dynamical behaviour of linear discrete-time singular systems. Combining the basic theory of Drazin inverse and the results reported in the case of the discrete time linear systems (see Hmamed, 1997), both necessary and sufficient conditions are established ensuring the componentwise asymptotic (exponential) stability. In addition, numerical examples are proposed to illustrate the correctness of the obtained results.