Determination of positive realizations with reduced numbers of delays or without delays for discrete-time linear systems

Stabilization of discrete-time LTI positive systems

“…The closed-loop system (11), (12) is stable strictly positive if the system (1), (2) is strictly positive and there exists positive definite diagonal matrices P P P,…”

“…Applicable methods for stabilization of positive linear discrete-time systems, maintaining its positivity when using linear state feedback, are given in [10], [11], [12].…”

Positive realizations with reduced numbers of delays for 2D continuous-discrete linear systems

“…. ., n − 1 satisfying (24) and find nonnegative matrices B 0 , B j,0 , B 0,k , j = 0, 1, ..., q 1 , k = 0, 1, ..., q 2 and the matrix C defined by (21).…”

“…A new modified state variable diagram method for determination of positive realizations with the reduced number of delays for given proper transfer matrices of continuous-time linear systems has been proposed in [23]. An extension of this method for discrete-time linear systems is given in [24].…”

A new approach to the realization problem for fractional discrete-time linear systems

“…An overview of the positive realization problem is given in [1,2,6,9]. The realization problem for positive continuous-time and discrete-time linear system has been considered in [6,7,[10][11][12][13][14][15][16][17][18][19][20][21][22] and for linear systems with delays in [6,10,15,[21][22][23][24]. The realization problem for fractional linear systems has been analyzed in [6,7,[25][26][27][28][29][30] for positive 2D hybrid linear systems in [24,31,32] and for fractional systems with delays in [33,34].…”