Consider the data set given in Example 10.2. Assume that the system has three poles and two zeros. One of the poles is at z = 0.1 and one of the zeros is at z = 0.10002. Identify the system transfer function. Compare the estimated values of the two remaining poles with those given in Example 10.2.

Example 10.2

Consider the following impulse response data for a SISO discrete-time LTI system with
a sampling time of T = 0.01 s. The output is measured at the sampling time instants
t = 0, 0.01, 0.02, c, 0.08, as shown in Fig. 10-2.

k y(k) 0 0 1 0.996 2 -0.298 3 4 5 6 7 8 -0.0148 0.0338 -0.0081 -0.0011 0.0011 -0.0002 Our objective is to identify a similarity transformation of the system matrices A, B, and C, and the corresponding transfer function, using the given values of y(k) and with the information