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The following model has been proposed to describe the motion of a constant-velocity guided missile:

y - [0 0 0 1 0]x.

(a) Verify that the system is not controllable by analyzing the controllability matrix using the ctrb function.

(b) Develop a controllable state variable model by first computing the transfer function from u to y, then cancel any common factors in the numerator and denominator polynomials of the transfer function. With the modified transfer function just obtained, use the ss function to determine a modified state variable model for the system.

(c) Verify that the modified state variable model in part (b) is controllable.

(d) Is the constant velocity guided missile stable?

(e) Comment on the relationship between the controllability and the complexity of the state variable model (where complexity is measured by the number of state variables).

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