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Consider the nonautonomous system x₁ = −x₁ + x₂ + (x₁²³ + x₂²) sint x₂ = −x₁₁ - x₂ + (x₁²+x2₂²) cost Show that the origin is exponentially stable. Is the origin globally exponentially stable?

Consider the nonautonomous system x₁ = −x₁ + x₂ + (x₁²³ + x₂²) sint x₂ = −x₁₁ - x₂ + (x₁²+x2₂²) cost Show that the origin is exponentially stable. Is the origin globally exponentially stable?

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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Consider the nonautonomous system 2 x₁ = − x₁ + x₂ + (x₂₁² + x₂²) sint x₂ =−x₁ − x₂ + (x₁² + x₂²) cost Show that the origin is exponentially stable. Is the origin globally exponentially stable?
Transcribed Image Text:Consider the nonautonomous system 2 x₁ = − x₁ + x₂ + (x₂₁² + x₂²) sint x₂ =−x₁ − x₂ + (x₁² + x₂²) cost Show that the origin is exponentially stable. Is the origin globally exponentially stable?
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