The paper analyzes a partial case of a delayed linear three-dimensional discrete system z(k + 1) = Az(k) + Bz(k −1) + u(k), k = 0, 1,…}, where A and B are constant 3 by 3 matrices, u: {0, 1, … } → ℝ3 and z: {−1, 0, … }→ ℝ3. Matrices A, B and function u are specified in such a way that the system is a discrete analogue of a differential model of the Mach number dynamics concerning a time-optimal control of a high-speed closed-circuit wind tunnel. The general solution is found by transforming this system into a solvable non-delayed one.

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