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Content available Stability of convex linear combinations of continuous-time and discrete-time linear systems
Kaczorek Tadeusz
Archives of Control Sciences
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2023
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Vol. 33, No. 4
789--799
EN
The asymptotic stability of the convex linear combination of continuous-time and discrete-time linear systems is considered. Using the Gershgorin theorem it is shown that the convex linear combination of the linear asymptotically stable continuous-time and discretetime linear systems is also asymptotically stable. It is shown that the above thesis is also valid (even simpler) for positive linear systems.
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Content available Convex linear combination of the controllability pairs for linear systems
Kaczorek Tadeusz, Klamka Jerzy
Control and Cybernetics
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2021
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Vol. 50, No. 4
541--551
EN
The convex linear combination of the controllability pairs of linear continuous-time linear systems is defined and its properties are discussed. The main result is obtained using pure algebraic methods. In the illustrative examples different cases of linear convex combinations are analyzed.
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