Consider the system of Problem, given by(a) Find the transfer function for this system.(b)...

Consider the system of Problem, given by

(a) Find the transfer function for this system.

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(b) Use a similarity transformation to find a different state model for this system.

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(c) Use MATLAB to verify the results of Parts (a) and (b).

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(d) Calculate the transfer function of Part (b). This function should equal that of Part (a).

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(e) Verify the results in Part (d) using MATLAB.

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(f) You have just verified Property 4, (13.64), of similarity transformations. Verify the other three properties in (13.61), (13.62), and (13.63).

Consider the system described by the state equations

(a) Find the state transition matrix.

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(b) Verify the results of Part (a), using a different procedure.

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(c) Find the initial-condition response for x(0) = [1 2]T.

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(d) Verify the calculation of the state vector x[n] in Part (c), by substitution in the equation x[n + 1] = Ax[n].

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(e) Calculate the system unit step response, with x(0) = 0, using iteration.

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(f) Calculate the system unit step response, with x(0) = 0, using (13.32).

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(g) Verify the results of Parts (e) and (f), using the system transfer function and the z-transform.

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(h) Verify the results in Part (g) using MATLAB.