Using the data given in Problem 10.5-1, derive the state-variable model using the algorithm described in Section 10.4.

Problem 10.5-1

(a) A first-order system yields the following input–output measurements:

Find the system transfer function by the least-squares batch procedure, using all the data.

(b) An additional data pair for k = 3 is measured, with the input equal to zero and the output equal to 31.8. Start the recursive least-squares procedure using the results of part (a), and calculate #n using the additional data pair.

k 0 1 2 Input 10 10 10 Output 0 12.2 20.1