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(A simple feedback system) Consider the two systems: H{} and G{} whose input- output relationships are given as follows. y₁(t) = H{x₁(t)} = t²x₁(t), y2(t) = G{x₂(t)} = ax₂(t) (Part a) Determine if the system H{} is BIBO stable. x(t) + z(t) H{} G{.} y(t) Now consider the feedback system as given in the layout below. (Part b) Derive the input-output relationship of the feedback system. You are expected to provide an expression relating y(t) to x(t). Hint: It helps to define the output of the system G{} as z(t) (see Figure) and trying to relate y(t) to x(t) and z(t). Now try to remove z(t) based on it being the output of G{.}. (Part c) For a < 0, is the system stable ?

(A simple feedback system) Consider the two systems: H{} and G{} whose input- output relationships are given as follows. y₁(t) = H{x₁(t)} = t²x₁(t), y2(t) = G{x₂(t)} = ax₂(t) (Part a) Determine if the system H{} is BIBO stable. x(t) + z(t) H{} G{.} y(t) Now consider the feedback system as given in the layout below. (Part b) Derive the input-output relationship of the feedback system. You are expected to provide an expression relating y(t) to x(t). Hint: It helps to define the output of the system G{} as z(t) (see Figure) and trying to relate y(t) to x(t) and z(t). Now try to remove z(t) based on it being the output of G{.}. (Part c) For a < 0, is the system stable ?

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 simple feedback system) Consider the two systems: H{} and G{} whose input- output relationships are given as follows. y₁(t) = H{x₁(t)} = t²x₁(t), (Part a) Determine if the system x(t) + z(t) H{.} is BIBO stable. H{.} Y2(t) = G{x2(t)} = ax₂(t) G{.} y (t) Now consider the feedback system as given in the layout below. (Part b) Derive the input-output relationship of the feedback system. You are expected to provide an expression relating y(t) to x(t). Hint: It helps to define the output of the system G{} as z(t) (see Figure) and trying to relate y(t) to x(t) and z(t). Now try to remove z(t) based on it being the output of G{.}. (Part c) For a < 0, is the system stable ?
Transcribed Image Text:(A simple feedback system) Consider the two systems: H{} and G{} whose input- output relationships are given as follows. y₁(t) = H{x₁(t)} = t²x₁(t), (Part a) Determine if the system x(t) + z(t) H{.} is BIBO stable. H{.} Y2(t) = G{x2(t)} = ax₂(t) G{.} y (t) Now consider the feedback system as given in the layout below. (Part b) Derive the input-output relationship of the feedback system. You are expected to provide an expression relating y(t) to x(t). Hint: It helps to define the output of the system G{} as z(t) (see Figure) and trying to relate y(t) to x(t) and z(t). Now try to remove z(t) based on it being the output of G{.}. (Part c) For a < 0, is the system stable ?
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