Recent Developments in Reachability and Controllability of Positive Linear Systems
نویسندگان
چکیده
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
منابع مشابه
Reachability indices of positive linear systems
It is well known that positive linear systems have differences in the concepts and characterizations of the structural properties of reachability and controllability. In this paper, the reachability indices of a positive system are defined and consequently they are studied. For that, a canonical form of the reachability indices is given by positive similarity. From that canonical form, it is es...
متن کاملReachability and controllability of positive fractional-order discrete-time systems
In the paper the positive linear discrete-time noncommensurate fractional-order systems described by the state equations are considered. Definition and necessary and sufficient conditions for the positivity, reachability and controllability to zero are given and proven. The considerations are illustrated by a numerical example.
متن کاملOn Reachability of Positive Linear Discrete-Time Systems with Scalar Controls
Positive systems are defined as systems in which the state trajectory is always positive (or at least non-negative) whenever the initial state is positive (nonnegative). Positive linear systems are defined on cones and not on linear spaces and that is why the reachability and controllability tests for linear systems prove to be false. In this paper necessary and sufficient condition for reachab...
متن کاملRealization Problem for Positive Linear Systems with Time Delay
In positive systems inputs, state variables and outputs take only nonnegative values. Examples of positive systems are industrial processes involving chemical reactors, heat exchangers and distillation columns, storage systems, compartmental systems, water and atmospheric pollution models. A variety of models having positive linear systems behavior can be found in engineering, management scienc...
متن کاملRealization Problem for Positive Multivariable Discrete–time Linear Systems with Delays in the State Vector and Inputs
In positive systems, inputs, state variables and outputs take only non-negative values. Examples of positive systems are industrial processes involving chemical reactors, heat exchangers and distillation columns, storage systems, compartmental systems, water and atmospheric pollution models. A variety of models having positive linear systems behaviour can be found in engineering, management sci...
متن کامل