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The problem of existence of reachable pairs (A, B) of discrete-time linear systems is formulated and solved. Necessary and sufficient conditions for the reachability of standard and positive full order and fractional order discrete-time linear systems are recalled. The existence of the reachable pairs (A, B) of the systems is investigated. Considerations are illustrated by numerical examples.
A new class of positive 2D Roesser type models is introduced. Necessary and sufficient conditions are established for the reachability of the positive 2D Roesser type model for zero boundary conditions. It is shown that the positive 2D Roesser type model having not nilpotent system matrix is unreachable for nonzero boundary conditions. The minimum energy control problem is formulated and solved for...
The minimum energy control problem for the fractional positive continuous-time linear systems is formulated and solved. Sufficient conditions for the existence of solution to the problem are established. A procedure for solving of the problem is proposed and illustrated by numerical examples.
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