Controllability and minimum energy control of linear fractional discrete-time infinite-dimensional systems

The main purpose of the paper is to discuss controllability problem for infinite-dimensional fractional linear discrete-time control systems. Moreover, the minimum energy control problem of infinite-dimensional fractional-discrete time linear systems is also addressed. Using theory of linear operators necessary and sufficient conditions for the exact controllability of the system are established. Sufficient conditions for the solvability of the minimum energy control of the infinite-dimensional fractional discrete-time systems are given. A procedure for computation of the optimal sequence of inputs minimizing the quadratic performance index is proposed.