Positive state controllability of positive linear systems (original) (raw)

Positive controllability of positive dynamical systems

Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301), 2002

... of Infinite Dimensional Systems", vol.I and vol ... of Distributed Parameter Systems", Toulouse (France ... J., "Controllability of Dynamical Systems", Kluwer Academic ...

On controllability of linear systems with positive control

IFAC Proceedings Volumes, 2005

Necessary conditions for the controllability on linear systems with positive control are presented. The real case is analyzed and the Jordan form representation is employed. The minimum number of necessary controls to obtain controllability is remarked.

Positive output controllability of linear discrete–time invariant systems

Control and Cybernetics

This paper studies the output controllability of discrete linear time invariant systems (LTI) with non-negative input constraints. Some geometrical arguments and positive invariance concepts are used to derive the necessary and/or sufficient conditions for the positive output controllability of discrete LTI systems. The paper also provides several academic examples, which support the theoretical results.

Recent developments in reachability and controllability of positive linear systems

Proceedings of the 15th IFAC World Congress, 2002, 2002

In this paper, recent results on the structural properties of positive linear systems are collected and analyzed. The study of reachability and controllability properties of positive invariant linear systems is focussed, mainly, in the recent years, either for discrete and continuous systems when results are known. In addition, all known results of positive periodic linear systems are discussed in the paper. Those results are discussed either with algebraic and combinatorial approaches. Canonical forms of reachability for positive invariant and periodic discrete-time linear systems are displayed and analyzed. Finally, the essential reachability and controllability properties are studied for both kind of systems. ©IFAC 2002

On the positive realization of controllable behaviors

Proceedings of the 15th IFAC World Congress, 2002, 2002

Positive linear systems, traditionally investigated within the state-space framework, have been recently analyzed within the behavioral setting, by focusing the attention on the autonomous case. Also, the positive realization problem has been fully explored in the special case of autonomous behaviors. In this contribution, we focus our attention on controllable behaviors. We first address the general realization problem by means of driving variable state-space representations and later analyze the possibility of realizing a controllable behavior by means of a positive driving variable representation. Several necessary and sufficient conditions for problem solvability are presented.

APPROXIMATE CONTROLLABILITY WITH POSITIVE CONTROLS

1997

In this paper, controllability of the linear discrete-time systems (A,B,Ω):x k+1 =Ax k +Bu k , x k ∈X, u k ∈Ω, is studied, where X is a Banach space and the control set Ω is assumed to be a cone in a Banach space U . Some criteria for approximate controllability are given. The case where the operator A is compact is examined in detail by using the spectral decomposition of the state space X. As a result, a criterion for approximate controllability of (A,B,Ω) is obtained without imposing a restrictive condition that the system with no control constraints (A,B,U ) is exactly controllable. The obtained results are then applied to consider the problem of controllability for linear functional differential equations with positive controls. Some necessary and sufficient conditions of approximate controllability to the state space R n ×L p are presented and some illustrating examples are given.

On stability and reachability of perturbed positive systems

Advances in Difference Equations, 2014

This paper deals mainly with the structural properties of positive reachability and stability. We focus our attention on positive discrete-time systems and analyze the behavior of these systems subject to some perturbation. The effects of permutation and similar transformations are discussed in order to determine the structure of the perturbation such that the closed-loop system is positively reachable and stable. Finally, the results are applied to Leslie's population model. The structure of the perturbation is shown such that the properties of the original system remain and an explicit expression of its set of positively reachable populations is given.