Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
Consider the two-input nonlinear system żey 1 x = u ý = v Use the center manifold theory to prove that the two-input system is locally asymptotically stabi- lizable by u==x+az² v==y+B₂³ with suitable coefficients a and 3. Hint: Take advantage of the property of an exponential function. (ii) Use the adding an integrator technique to design a smooth state feedback control law u= u(z, x, y), v = v(z, x, y), with u(0,0,0) = 0 and v(0, 0, 0) = 0, globally asymptotically stabilizing the system. Hint: Observe that, for instance, the virtual controller x* = -2 y* = 2² globally asymptotically stabilizes the z-subsystem.

Consider the two-input nonlinear system żey 1 x = u ý = v Use the center manifold theory to prove that the two-input system is locally asymptotically stabi- lizable by u==x+az² v==y+B₂³ with suitable coefficients a and 3. Hint: Take advantage of the property of an exponential function. (ii) Use the adding an integrator technique to design a smooth state feedback control law u= u(z, x, y), v = v(z, x, y), with u(0,0,0) = 0 and v(0, 0, 0) = 0, globally asymptotically stabilizing the system. Hint: Observe that, for instance, the virtual controller x* = -2 y* = 2² globally asymptotically stabilizes the z-subsystem.

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...
See similar textbooks
icon
Related questions
Question
Consider the two-input nonlinear system żey 1 x = u ý = v (i) Use the center manifold theory to prove that the two-input system is locally asymptotically stabi- lizable by u=−x+az² v=-y + B₂³ with suitable coefficients a and B. Hint: Take advantage of the property of an exponential function. (ii) Use the adding an integrator technique to design a smooth state feedback control law u= u(z, x, y), v = v(z, x, y), with u(0, 0, 0) = 0 and v(0,0,0) = 0, globally asymptotically stabilizing the system. Hint: Observe that, for instance, the virtual controller 2* = -2 y* = 2² globally asymptotically stabilizes the z-subsystem.
Transcribed Image Text:Consider the two-input nonlinear system żey 1 x = u ý = v (i) Use the center manifold theory to prove that the two-input system is locally asymptotically stabi- lizable by u=−x+az² v=-y + B₂³ with suitable coefficients a and B. Hint: Take advantage of the property of an exponential function. (ii) Use the adding an integrator technique to design a smooth state feedback control law u= u(z, x, y), v = v(z, x, y), with u(0, 0, 0) = 0 and v(0,0,0) = 0, globally asymptotically stabilizing the system. Hint: Observe that, for instance, the virtual controller 2* = -2 y* = 2² globally asymptotically stabilizes the z-subsystem.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Root Locus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,
SEE MORE TEXTBOOKS