5. Try to find a strict (LƒV < 0) Liapunov's function for equilibrium (0,0)in a small disk centered at the origin for systemSx²= -2x - y²y' = -y-x².What is the maximal disk for which your construction works?

The differential equation is given below.We need to find a strict Liapunov's function for…

Answered: Try to find a strict (LƒV < 0)…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

5. Try to find a strict (LƒV < 0) Liapunov's function for equilibrium (0,0)
in a small disk centered at the origin for system
Sx²
= -2x - y²
y' = -y-x².
What is the maximal disk for which your construction works?

Expert Solution

Step 1: Introduction

The differential equation is given below.

$table row cell x apostrophe end cell equals cell negative 2 x minus y squared end cell row cell y apostrophe end cell equals cell negative y minus x squared end cell end table$

We need to find a strict $open parentheses script capital l subscript f V less than 0 close parentheses$ Liapunov's function for equilibrium $open parentheses 0 comma 0 close parentheses$ in a small disk centered at the origin for the above system