Verify that V = x14+ 2x22+2x1x2 + x12 is a Lyapunov function for the system described by the following state equations dx1/dt = x2 dx2/dt= -x2 - x13. Then, check the stability of the system.
Verify that V = x14+ 2x22+2x1x2 + x12 is a Lyapunov function for the system described by the following state equations dx1/dt = x2 dx2/dt= -x2 - x13. Then, check the stability of the system.
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter5: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 5CC
Related questions
Question
Verify that
V = x14+ 2x22+2x1x2 + x12
is a Lyapunov function for the system described by the following state
equations
dx1/dt = x2
dx2/dt= -x2 - x13.
Then, check the stability of the system.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning