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...

Positive systems play an important role in and control theory have found many applications multiagent systems, neural networks, biology, more. map the nonnegative orthant to itself (and also nonpositive itself). In other words, they set of vectors with zero sign variations itself. this article, discrete-time linear that up k - 1 are introduced. For special case = these reduce positive systems. ...

Abstract We prove new characterisations of exponential stability for positive linear discrete-time systems in ordered Banach spaces, terms small-gain conditions. Such conditions have played an important role the finite-dimensional theory, but are relatively unexplored infinite-dimensional setting, yet. Our results applicable to spaces that a normal and generating cone. Moreover, we show our cri...

The paper provides extended methods for control linear positive discrete-time systems that are subject to parameter uncertainties, reflecting structural system constraints and properties when solving the problem of quadratic stability. By using an extension Lyapunov approach, stability is presented become apparent in pre-existing positivity design feedback control. approach prefers representati...