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1

Invariant properties of positive linear electrical circuits

Kaczorek Tadeusz

Archives of Electrical Engineering

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2019

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Vol. 68, nr 4

875--890

EN

The invariant properties of the stability, reachability, observability and transfer matrices of positive linear electrical circuits with integer and fractional orders are investigated. It is shown that the stability, reachability, observability and transfer matrix of positive linear systems are invariant under their integer and fractional orders.

2

Analysis of positive linear continuous-time systems using the conformable derivative

Kaczorek T.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 2

335--340

EN

Positive linear continuous-time systems are analyzed via conformable fractional calculus. A solution to a fractional linear system is derived. Necessary and sufficient conditions for the positivity of linear systems are established. Necessary and sufficient conditions for the asymptotic stability of positive linear systems are also given. The solutions of positive fractional linear systems based on the Caputo and conformable definitions are compared.

3

On the stability of continuous-time positive switched systems with rank one difference

Fornasini E., Valcher M. E.

Control and Cybernetics

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2013

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Vol. 42, no. 1

47--62

EN

Continuous-time positive systems, switching among p subsystems whose matrices differ by a rank one matrix, are introduced, and a complete characterization of the existence of a common linear copositive Lyapunov function for all the subsystems is provided. Also, for this class of systems it is proved that a well-known necessary condition for asymptotic stability, namely the fact that All convex combinations of the system matrices are Hurwitz, becomes equivalent to the generally weaker condition that the systems matrices are Hurwitz. In the special case of two-dimensional systems, this allows for drawing a complete characterization of asymptotic stability. Finally, the case when there are only two subsystems, possibly with commuting matrices, is investigated.

4

Reachability and controllability of compartmental systems.

James G., Rumchev V.

Systems Science

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2000

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Vol. 26, nr 1

5-13

EN

Compartmental models are frequently used in biology and medicine to analyze the behaviour of complex physiological systems and some of their properties (equilibrium points, stability, predicting the impact of different inflows) are well studied. Attempts have also been made to understand reachability and controllability properties of such models by employing the tests for linear systems. Linear compartmental systems as positive systems belong to the class of constrained linear systems, which are actually non-linear, and hence the reason why the general reachability and controllability tests developed for linear systems are fallible. In the paper, reachability and controllability properties of compartmental systems are studied by using some results in controllability theory for positive linear system. In particular, positive reachability and controllability criteria are in a digraph form, most suitable to the commonly used digraph representation of compartmental systems. Some specific compartmental models are also considered. The results obtained in the paper increase not only our understanding of the properties of compartmental models but they are also important for implementing feedback and optimal control strategies.

5

Reachability and Controlability of Positive Linear Systems with State Feedbacks

Kaczorek T.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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1999

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Vol. 47, nr 1

67-73

EN

It is shown that the reachability and controllability of positive linear systems is not invariant under the state-feedbacks.