Controllability for positive discrete–time linear systems with positive state*
نویسندگان
چکیده
Controllability of componentwise nonnegative discrete-time linear systems is considered. The key difference here from the well-established positive systems theory is that we permit the case where the input takes negative values, provided that the state remains nonnegative. Such a framework is very natural, moreover necessary, in situations such as population ecology to describe the control actions of harvesting or culling. The present contribution summarises recently published material by the authors and considers a novel application in low-gain PI control.
منابع مشابه
Optimal Finite-time Control of Positive Linear Discrete-time Systems
This paper considers solving optimization problem for linear discrete time systems such that closed-loop discrete-time system is positive (i.e., all of its state variables have non-negative values) and also finite-time stable. For this purpose, by considering a quadratic cost function, an optimal controller is designed such that in addition to minimizing the cost function, the positivity proper...
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 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 the Properties of Reachability, Observability, Controllability, and Constructibility of Discrete-Time Positive Time-Invariant Linear Systems with Aperiodic Choice of the Sampling Instants
This paper investigates the properties of reachability, observability, controllability, and constructibility of positive discrete-time linear time-invariant dynamic systems when the sampling instants are chosen aperiodically. Reachability and observability hold if and only if a relevant matrix defining each of those properties is monomial for the set of chosen sampling instants provided that th...
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