2. For the following pair of coupled differential equationsa. Rewrite in a matrix form appropriate for a linear state space problem given that theand the input vector is U =12state vector is Xdl,= 31, +2I, +2v, +v2dtdl,-21, +41, +v,dtb. Calculate the controllability matrix, Mc for this system and determine if the system isstate controllable.

Answered: Image /qna-images/answer/3e08898b-3fd1-47f1-bbb6-a15d3749fc3b.jpg

2. For the following pair of coupled differential equations a. Rewrite in a matrix form appropriate for a linear state space problem given that the state vector is X = and the input vector is U : al = 31, +21, +2v, +v2 dt dI, --21, + 41, +v, dt %3D b. Calculate the controllability matrix, Mc for this system and determine if the system is state controllable.

2. For the following pair of coupled differential equations a. Rewrite in a matrix form appropriate for a linear state space problem given that the state vector is X = and the input vector is U : al = 31, +21, +2v, +v2 dt dI, --21, + 41, +v, dt %3D b. Calculate the controllability matrix, Mc for this system and determine if the system is state controllable.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 70EQ

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