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 systemx = 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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Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter1: Systems Of Linear Equations

Section1.1: Introduction To Systems Of Linear Equations

Problem 72E: Find a system of two equations in three variables, x1, x2 and x3 that has the solution set given by...

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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 : L(x,y) - 2(x² + y²) = .