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

Kaczorek T.

Acta Mechanica et Automatica

2011

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

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

International Journal of Applied Mathematics and Computer Science

2005

Vol. 15, no 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 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.

Reachability and controllability of time-variant discrete-time positive linear systems

Rumchev V. G., Adeane J.

Control and Cybernetics

2004

Vol. 33, no 1

85-94

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.