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Necessary and Sufficient Stability Conditions of Fractional Positive Continuous-Time Linear Systems

100%

Kaczorek T.

tom Vol. 5, no. 2

52-54

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.

Monomial subdigraphs of reachable and controllable positive discrete-time systems

88%

Bru R. , Caccetta L. , Rumchev V. G.

nr 1

159-166

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 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.

Dynamical properties of Metzler systems

88%

Mitkowski W.

nr 4

Stability and stabilization of positive linear dynamical systems: new equivalent conditions and computations

75%

Yang H. , Hu Y.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2020

tom Vol. 68, nr 2

307--315

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.