Fractional positive linear systems

Abstract

PurposeThe purpose of this paper is to introduce a new class of fractional positive continuous‐time and discrete‐time linear systems.Design/methodology/approachSolutions to the state equations of the fractional systems are given.FindingsNecessary and sufficient conditions are established for the internal and external positivity and of the reachability and controllability to zero of the fractional systems.Originality/valueA method for analysis of the fractional positive linear systems is proposed.

Descriptor fractional discrete-time linear system with two different fractional orders and its solution

“…Application of the Drazin inverse method to analysis of descriptor fractional discrete-time and continuous-time linear systems have been given in [19,20]. The positive fractional linear systems has been investigated in [21,22]. The positive linear systems with different fractional orders have been addressed in [23,24].…”

Remarks on Fractional Discrete Cone Control Systems with n-Orders and Their Stability

“…These systems appear frequently in practical applications as well as in real phenomena, among other in biology, medicine, economics, electrotechnics, control system design, etc. (see [6,7,13,25,26] and the references therein). The natural generalization of positive systems are cone systems, i.e., systems whose trajectories always remain in the given cone if they are initialized in this cone.…”

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

“…The realization problem for positive continuous-time and discrete-time linear systems has been considered in [5,[16][17][18][19] and the positive realization problem for discrete-time systems with delays in [9,10,20]. The fractional positive linear systems have been addressed in [11,21,22]. The realization problem for fractional linear systems has been analyzed in [7] and for positive 2D hybrid systems in [8].…”