Consider the system described in Problem 2.10-2.

(a) Find the transfer function of this system.

(b) Let u(k) = 1, k ≥0 (a unit step function) and x(0) = 0 . Use the transfer function of part (a) to find the system response.

(c) Find the state transition matrix Φ(k) for this system.

(d) Use (2-90) to verify the step response calculated in part (b). This calculation results in the response expressed as a summation. Then check the values y(0), y(1) , and y(2).

(e) Verify the results of part (d) by the iterative solution of the state equations.

Equation 2-90

Problem 2.10-2

Consider the system described by

x(k+ 1) = | (*) + [ ]-(*) 01 03 y(x) = [-2 1 ]x(*)