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Consider the second-order system: dx₁ dt = -ax₁, dx₂ dt 1 1 V₁(x) == x² + x², = = -bx₁-CX₂ where a, b, c > 0. a) Investigate whether the functions V₁ (x) and V₂ (x) are Lyapunov functions for the system and give any conditions that must hold 1 V₂(x) = = x² + ²/(x₂ + 2 baxı)² c

Consider the second-order system: dx₁ dt = -ax₁, dx₂ dt 1 1 V₁(x) == x² + x², = = -bx₁-CX₂ where a, b, c > 0. a) Investigate whether the functions V₁ (x) and V₂ (x) are Lyapunov functions for the system and give any conditions that must hold 1 V₂(x) = = x² + ²/(x₂ + 2 baxı)² c

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Consider the second-order system: dx₁ dt = -ax₁, dx2 dt 1 1 V₂(x) = x² + 2x², .= -bx₁ - CX₂ where a, b, c > 0. a) Investigate whether the functions V₁ (x) and V₂ (x) are Lyapunov functions for the system and give any conditions that must hold 2 b V2₂(x) = ² x ² + 1 ² ( x ₂ + _ _ _ _ x₁1) ² -X1 2 c - a
Transcribed Image Text:Consider the second-order system: dx₁ dt = -ax₁, dx2 dt 1 1 V₂(x) = x² + 2x², .= -bx₁ - CX₂ where a, b, c > 0. a) Investigate whether the functions V₁ (x) and V₂ (x) are Lyapunov functions for the system and give any conditions that must hold 2 b V2₂(x) = ² x ² + 1 ² ( x ₂ + _ _ _ _ x₁1) ² -X1 2 c - a
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