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1
Content available Stability and stabilization of positive linear dynamical systems: new equivalent conditions and computations
Yang H., Hu Y.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2020
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Vol. 68, nr 2
307--315
EN
New equivalent conditions of the asymptotical stability and stabilization of positive linear dynamical systems are investigated in this paper. The asymptotical stability of the positive linear systems means that there is a solution for linear inequalities systems. New necessary and sufficient conditions for the existence of solutions of the linear inequalities systems as well as the asymptotical stability of the linear dynamical systems are obtained. New conditions for the stabilization of the resultant closed-loop systems to be asymptotically stable and positive are also presented. Both the stability and the stabilization conditions can be easily checked by the so-called I-rank of a matrix and by solving linear programming (LP). The proposed LP has compact form and is ready to be implemented, which can be considered as an improvement of existing LP methods. Numerical examples are provided in the end to show the effectiveness of the proposed method.
2
Content available Necessary and Sufficient Stability Conditions of Fractional Positive Continuous-Time Linear Systems
Kaczorek T.
Acta Mechanica et Automatica
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2011
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Vol. 5, no. 2
52-54
EN
Necessary and sufficient conditions for the asymptotic stability of fractional positive continuous-time linear systems are established. It is shown that the matrix A of the stable fractional positive system has not eigenvalues in the part of stability region located in the right half of the complex plane.
3
Content available Pointwise completeness and pointwise degeneracy of standard and positive linear systems with state-feedbacks
Kaczorek T.
Journal of Automation Mobile Robotics and Intelligent Systems
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2010
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Vol. 4, No. 1
3-7
EN
The pointwise completeness and pointwise degeneracy of standard and positive linear discrete-time and continuous- time systems with state-feedbacks are addressed. It is shown that: 1) the pointwise completeness and pointwise degeneracy of continuous-time standard systems are invariant under the state and output feedbacks, 2) for standard and positive discrete-time and positive continuous- time systems necessary and sufficient conditions are established for the existence of gain matrices of statefeedbacks such that the closed-loop systems are pointwise complete. Considerations are illustrated by numerical examples.
4
Content available remote Dynamical properties of Metzler systems
Mitkowski W.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2008
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Vol. 56, nr 4
309-312
EN
Spectral properties of nonnegative and Metzler matrices are considered. The conditions for existence of Metzler spectrum in dynamical systems have been established. An electric RL and GC ladder-network is presented as an example of dynamical Metzler system. The suitable conditions for parameters of these electrical networks are formulated. Numerical calculations were done in MATLAB.
5
Content available remote Monomial Subdigraphs of Reachable and Controllable Positive Discrete-time Systems
Bru R., Cacetta L., Rumchev V. G.
International Journal of Applied Mathematics and Computer Science
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2005
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Vol. 15, no 1
159-166
EN
A generic structure of reachable and controllable positive linear systems is given in terms of some characteristic components (monomial subdigraphs) of the digraph of a non-negative a pair. The properties of monomial subdigraphs are examined and used to derive reachability and controllability criteria in a digraph form for the general case when the system matrix A may contain zero columns. The graph-theoretic nature of these criteria makes them computationally more efficient than their known equivalents. The criteria identify not only the reachability and controllability properties of positive linear systems, but also their reachable and controllable parts (subsystems) when the system does not possess such properties.
6
Content available remote Reachability and controllability of time-variant discrete-time positive linear systems
Rumchev V. G., Adeane J.
Control and Cybernetics
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2004
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Vol. 33, no 1
85-94
EN
In this paper necessary and sufficient conditions (and criteria) for null-controllability, reachability and controllability of time-variant discrete-time positive linear systems are established. These properties appear to be entirely structural properties, that is, they do depend on the zero-nonzero pattern of the pair (A(k), B[k)) > 0 and do not depend on the values of its entries. An interesting phenomenon has been revealed namely the time needed to reach the origin for a null-controllable system as well as the time to reach a (non-negative) state from the origin for a reachable system can be less, equal or greater than the dimension of the system. This phenomenon has no equivalent in the case of time-invariant discrete-time positive linear systems where this time is always less or equal to the system dimension. Examples are provided.
7
A fractional-flow model of serial manufacturing systems with rework and its reachability and controllability properties
James G., Rumchev V.
Systems Science
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2001
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Vol. 27, nr 2
49-59
EN
A dynamic fractional-flow model of a serial manufacturing system incorporating rework is considered. Using some recent results on reachability and controllability of positive linear systems the ability of serial manufacturing systems with rework to "move in space", that is their reachability and controllability properties, are studied. These properties are important not only for optimising the performance of the manufacturing system, possibly off-line, but also to improve its functioning by using feedback control on-line.
8
Content available Remarks on stability of positive linear systems
Mitkowski W.
Control and Cybernetics
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2000
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Vol. 29, no 1
295-304
EN
Spectral properties of nonegative matrices are considered. Asymptotic stability and stabilisation problems of positive discrete-time and continous-time linear systems by feedbacks are discussed. The electric RC-networks are presented as examples of positive systems. Numerical calculations were made using the MATLAB program.
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