Algebraic and transfer-function criteria of fixed-time controllability of delay-differential systems†

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Abstract
Sufficient algebraic and transfer-function criteria of fixed-time controllability of linear time-invariant delay-differential system of the form [xdot](t) = Ax(t) + Bx(t-h) + Cu(t),x(t)∊Rn u(t)eRm are given. It is shown that those criteria are also necessary if the system is pointwise complete. It is known that if (1) rank B=l, (2) rank B = n,(3) n = 2, the above system is always point-wise complete and in these cases the algebraic and transfer function criteria of fixed-time controllability are both necessary and sufficient.

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