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Consider a discrete-time system described by: where x(k), x2(k) and xz(k) are the states and u(k) is the input. Find the necessary and sufficient conditions

Consider a discrete-time system described by:

where x(k), x2(k) and xz(k) are the states and u(k) is the input. Find the necessary and sufficient conditions on a, b, and c so that the system is controllable. Justify your answer.

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