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Positivity and linearization of a class of nonlinear continuous-time systems by state feedbacks

100%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2015
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tom 25
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nr 4
827-831
EN
The positivity and linearization of a class of nonlinear continuous-time system by nonlinear state feedbacks are addressed. Necessary and sufficient conditions for the positivity of the class of nonlinear systems are established. A method for linearization of nonlinear systems by nonlinear state feedbacks is presented. It is shown that by a suitable choice of the state feedback it is possible to obtain an asymptotically stable and controllable linear system, and if the closed-loop system is positive then it is unstable.
2
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Simple conditions for practical stability of positive fractional discrete-time linear systems

86%
Busłowicz M., Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2009
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tom 19
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nr 2
263-269
EN
In the paper the problem of practical stability of linear positive discrete-time systems of fractional order is addressed. New simple necessary and sufficient conditions for practical stability and for practical stability independent of the length of practical implementation are established. It is shown that practical stability of the system is equivalent to asymptotic stability of the corresponding standard positive discrete-time systems of the same order. The discussion is illustrated with numerical examples.
3
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Residuation in orthomodular lattices

86%
Chajda I., Länger H.
Topological Algebra and its Applications
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2017
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tom 5
|
nr 1
1-5
EN
We show that every idempotent weakly divisible residuated lattice satisfying the double negation law can be transformed into an orthomodular lattice. The converse holds if adjointness is replaced by conditional adjointness. Moreover, we show that every positive right residuated lattice satisfying the double negation law and two further simple identities can be converted into an orthomodular lattice. In this case, also the converse statement is true and the corresponence is nearly one-to-one.
4
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Positive stable realizations of fractional continuous-time linear systems

86%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
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2011
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tom 21
|
nr 4
697-702
EN
Conditions for the existence of positive stable realizations with system Metzler matrices for fractional continuous-time linear systems are established. A procedure based on the Gilbert method for computation of positive stable realizations of proper transfer matrices is proposed. It is shown that linear minimum-phase systems with real negative poles and zeros always have positive stable realizations.
5
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Externally and internally positive singular discrete-time linear systems

86%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
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2002
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tom 12
|
nr 2
197-202
EN
Notions of externally and internally positive singular discrete-time linear systems are introduced. It is shown that a singular discrete-time linear system is externally positive if and only if its impulse response matrix is non-negative. Sufficient conditions are established under which a single-output singular discrete-time system with matrices in canonical forms is internally positive. It is shown that if a singular system is weakly positive (all matrices E, A, B, C are non-negative), then it is not internally positive.
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