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A)Transform the following state space model into Diagonal Canonical Form (DCF) (that is, compute ADCF, BDCF, and CDCF):  (b) Use the ADCF matrix that you computed in part (a) to determine the matrix exponential exp(ADCF*t), and then use exp(ADCF*t) to compute the matrix exponential exp(At). (Note that exp(At) = eAt.) (c) Calculate the zero-input output component yzi(t) if the initial state is x(0) = [2 1]T. (d) Use your state space model in DCF to find the system transfer function, H(s).

A)Transform the following state space model into Diagonal Canonical Form (DCF) (that is, compute ADCF, BDCF, and CDCF):  (b) Use the ADCF matrix that you computed in part (a) to determine the matrix exponential exp(ADCF*t), and then use exp(ADCF*t) to compute the matrix exponential exp(At). (Note that exp(At) = eAt.) (c) Calculate the zero-input output component yzi(t) if the initial state is x(0) = [2 1]T. (d) Use your state space model in DCF to find the system transfer function, H(s).

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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A)Transform the following state space model into Diagonal Canonical Form (DCF) (that is, compute ADCF, BDCF, and CDCF): 

(b) Use the ADCF matrix that you computed in part (a) to determine the matrix exponential exp(ADCF*t), and then use exp(ADCF*t) to compute the matrix exponential exp(At). (Note that exp(At) = eAt.)
(c) Calculate the zero-input output component yzi(t) if the initial state is x(0) = [2 1]T.
(d) Use your state space model in DCF to find the system transfer function, H(s).

compute ADCF, BDCF, and CDCF): x = Ax + Bu, -3 A = [ ²7² 1²3], 1 y = Cx, C = [2 3] 3 = [ 2² ] B
Transcribed Image Text:compute ADCF, BDCF, and CDCF): x = Ax + Bu, -3 A = [ ²7² 1²3], 1 y = Cx, C = [2 3] 3 = [ 2² ] B
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