a) Determine if the system is controllable, using the Controllability matrix. b) Find the left eigenvectors of the system. c) Use the Eigenvector-Controllability test to verify your answer in part a. If the system is not controllable, which of the mode(s) are uncontrollable? Is the system stabilizable?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 30E
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Question 1: Consider the following system:
* (t) =
y(t) = [10] (t) + [0] u(t)
22] (t) + [1]u(t)
a) Determine if the system is controllable, using the Controllability matrix.
b) Find the left eigenvectors of the system.
c) Use the Eigenvector-Controllability test to verify your answer in part a. If the system is not
controllable, which of the mode(s) are uncontrollable? Is the system stabilizable?
Transcribed Image Text:Question 1: Consider the following system: * (t) = y(t) = [10] (t) + [0] u(t) 22] (t) + [1]u(t) a) Determine if the system is controllable, using the Controllability matrix. b) Find the left eigenvectors of the system. c) Use the Eigenvector-Controllability test to verify your answer in part a. If the system is not controllable, which of the mode(s) are uncontrollable? Is the system stabilizable?
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