Geodesic
Controllability of linear impulsive systems – an eigenvalue approach
Kybernetika, Tome 56 (2020) no. 4, pp. 727-752
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This article considers a class of finite-dimensional linear impulsive time-varying systems for which various sufficient and necessary algebraic criteria for complete controllability, including matrix rank conditions are established. The obtained controllability results are further synthesised for the time-invariant case, and under some special conditions on the system parameters, we obtain a Popov-Belevitch-Hautus (PBH)-type rank condition which employs eigenvalues of the system matrix for the investigation of their controllability. Numerical examples are provided that demonstrate--for the linear impulsive systems, null controllability need not imply their complete controllability, unlike for the non-impulsive linear systems.
This article considers a class of finite-dimensional linear impulsive time-varying systems for which various sufficient and necessary algebraic criteria for complete controllability, including matrix rank conditions are established. The obtained controllability results are further synthesised for the time-invariant case, and under some special conditions on the system parameters, we obtain a Popov-Belevitch-Hautus (PBH)-type rank condition which employs eigenvalues of the system matrix for the investigation of their controllability. Numerical examples are provided that demonstrate--for the linear impulsive systems, null controllability need not imply their complete controllability, unlike for the non-impulsive linear systems.
DOI : 10.14736/kyb-2020-4-0727
Classification : 15A18, 34A37, 93B05
Keywords: eigenvalues; impulses; controllability 
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S. Muni, Vijayakumar; K. George, Raju. Controllability of linear impulsive systems – an eigenvalue approach. Kybernetika, Tome 56 (2020) no. 4, pp. 727-752. doi: 10.14736/kyb-2020-4-0727

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