Consider the system of Problem.(a) Determine if this system is stable.(b) Give the system...

Consider the system of Problem.

(a) Determine if this system is stable.

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(b) Give the system modes.

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(c) Use MATLAB to check the results in Part (a).

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.