Consider the transfer function of a CT system given by 1.403 s(s+12) G(s) = Using a...

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Consider the transfer function of a CT system given by 1.403 s(s+12) G(s) = Using a zero-order hold with T = 0.01, the transfer function G(z) of the correspond- ing sampled-data system is given by G(z) 6.7426 x 10-5. = Yk z +0.9608 (z-1)(z- 0.8869) Show that a controllable and observable state-space realization of the system is given by Ik+1 = ] =* + [i] Ik 0 1 -0.8869 1.8869 = 6.7426 x 10-5 [0.9608 1] Tk. Uk i.e., verify that this state-space realization has the transfer function G(z) given above. Consider the transfer function of a CT system given by 1.403 s(s+12) G(s) = Using a zero-order hold with T = 0.01, the transfer function G(z) of the correspond- ing sampled-data system is given by G(z) 6.7426 x 10-5. = Yk z +0.9608 (z-1)(z- 0.8869) Show that a controllable and observable state-space realization of the system is given by Ik+1 = ] =* + [i] Ik 0 1 -0.8869 1.8869 = 6.7426 x 10-5 [0.9608 1] Tk. Uk i.e., verify that this state-space realization has the transfer function G(z) given above.

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