Minimum energy control of positive discrete-time linear systems with bounded inputs

A dynamical system is called positive if its trajectory starting from any nonnegative initial state remains forever in the positive orthant for all nonnegative inputs. An overview of state of the art in positive theory is given in the monographs [1, 2]. Variety of models having positive behavior can be found in engineering, economics, social sciences, biology and medicine, etc.. Positive linear systems consisting of n subsystems with different fractional orders have been analyzed in [3]. The minimum energy control problem for standard linear systems has been formulated and solved by J. Klamka [11-14] and for 2D linear systems with variable coefficients in [10]. The controllability and minimum energy control problem of fractional discrete-time linear systems has been investigated by Klamka in [14]. The minimum energy control of positive continuous-time linear systems has been addressed in [6]. The minimum energy control of positive fractional linear systems has been considered in [5] and of descriptor positive systems in [4, 8]. The minimum energy control of positive continuous-time linear systems with bounded inputs has been addressed in [7]. In this paper the minimum energy control problem for positive discrete-time linear systems with bounded inputs will be formulated and solved. The paper is organized as follows. In section 2 the basic definitions and theorems of the positive discrete-time linear systems are recalled and the necessary and sufficient conditions for the reachability