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1. Consider the following state-space system: -a₁ 1 [ ] Z(1) + [i ] T(1) r(t) -1 -a₂ [0 c] T(t) z(t) = y(t) =

1. Consider the following state-space system: -a₁ 1 [ ] Z(1) + [i ] T(1) r(t) -1 -a₂ [0 c] T(t) z(t) = y(t) =

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
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1. Consider the following state-space system: 1 _] 20(0) + [ 8 ] +60 i r(t) z(t) y(t) -α₁ = -1 -α2 = [0 c] T(t) (a) Suppose that r(t) is a unit step. Show that if -2<a₁-a₂ < 2 c‡0 then y(t) will contain an exponentially decaying sinusoid. (b) Suppose that r(t) = ku(t) is a step function. What conditions on a₁, a2 and c are necessary to ensure that lim y(t) = k Hint: Think about the Final Value Theorem and Transfer Function
Transcribed Image Text:1. Consider the following state-space system: 1 _] 20(0) + [ 8 ] +60 i r(t) z(t) y(t) -α₁ = -1 -α2 = [0 c] T(t) (a) Suppose that r(t) is a unit step. Show that if -2<a₁-a₂ < 2 c‡0 then y(t) will contain an exponentially decaying sinusoid. (b) Suppose that r(t) = ku(t) is a step function. What conditions on a₁, a2 and c are necessary to ensure that lim y(t) = k Hint: Think about the Final Value Theorem and Transfer Function
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