2- If L(x, y) = ax + by2 is a Lyapunov function at the origin for the system * = y + x³, y = -x + y³, a = b = 1. Then compute the expression :
2- If L(x, y) = ax + by2 is a Lyapunov function at the origin for the system * = y + x³, y = -x + y³, a = b = 1. Then compute the expression :
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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![2- If L(x, y) = ax + by2 is a Lyapunov function at the origin for the system
* = y + x³, y = -x + y²³, a = b = 1. Then compute the expression:
L(x, y) - 2(x + y4) =
3- If L(x, y) = ax² + by² is a Lyapunov function at the origin for the system
x = 2x + xy², y = y(1-x²), a = b = 1, then this system is:
(a) Stable (b) unstable (c) Asymptotic stable (d) stable if x < 0,y > 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcd37fe67-42f1-40af-98a8-3047ac04c640%2F3c5bf65c-7ab0-4e18-bfb0-7513bff34228%2Fv0zvlhj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2- If L(x, y) = ax + by2 is a Lyapunov function at the origin for the system
* = y + x³, y = -x + y²³, a = b = 1. Then compute the expression:
L(x, y) - 2(x + y4) =
3- If L(x, y) = ax² + by² is a Lyapunov function at the origin for the system
x = 2x + xy², y = y(1-x²), a = b = 1, then this system is:
(a) Stable (b) unstable (c) Asymptotic stable (d) stable if x < 0,y > 0.
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