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Which of the following functions V(y₁, Y2) is a Lyapunov function for the dynamical system with equilibrium point at (0, 0) y₁ = −2y₁y²e(¹1⁄₂)² — 6y₁, - Y2 y₂ = -2y²y₂e(¹1³2)² – 2y2

Which of the following functions V(y₁, Y2) is a Lyapunov function for the dynamical system with equilibrium point at (0, 0) y₁ = −2y₁y²e(¹1⁄₂)² — 6y₁, - Y2 y₂ = -2y²y₂e(¹1³2)² – 2y2

Advanced Engineering Mathematics
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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Which of the following functions equilibrium point at (0, 0) y₁ = −2y₁y²e(1132)² — 6y₁, V(y1, Y2) is a Lyapunov function for the dynamical system with Y2 y₂ = -2y²y₂e (₁₂)² – 2y₂ −2y²y2e(³1⁄2)²
Transcribed Image Text:Which of the following functions equilibrium point at (0, 0) y₁ = −2y₁y²e(1132)² — 6y₁, V(y1, Y2) is a Lyapunov function for the dynamical system with Y2 y₂ = -2y²y₂e (₁₂)² – 2y₂ −2y²y2e(³1⁄2)²
○ a. O b. ○ c. ○ d. V(y₁, y2) = e(4132)² V(y₁, Y2) = e(9192)² + y² − 1 + 3y² V(y₁, y2) = y₁ + (y2 − 1)² V(y₁, y2) = y²e(4192)² + y² − 3y₁
Transcribed Image Text:○ a. O b. ○ c. ○ d. V(y₁, y2) = e(4132)² V(y₁, Y2) = e(9192)² + y² − 1 + 3y² V(y₁, y2) = y₁ + (y2 − 1)² V(y₁, y2) = y²e(4192)² + y² − 3y₁
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