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Given the following Lyapunov candidate function, V = x"x and V = a"i + a"x = a" (A(t) + A" (t))æ < - a"x< -AV For the following system, show that for all t > 0 0 < x7x = V(t) < V(0)e¬mazt the system is asymptotically stable at the origin. i1 = -10x1 + etx2 i2 = -2x2

Given the following Lyapunov candidate function, V = x"x and V = a"i + a"x = a" (A(t) + A" (t))æ < - a"x< -AV For the following system, show that for all t > 0 0 < x7x = V(t) < V(0)e¬mazt the system is asymptotically stable at the origin. i1 = -10x1 + etx2 i2 = -2x2

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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3. Given the following Lyapunov candidate function, V = x"x and V = a" à + à"x = a" (A(t) + A" (t))æ < -Ax"x < -AV -Amazt the system is For the following system, show that for all t > 0 0 < x"x = V (t) < V(0)e¬^ asymptotically stable at the origin. *1 = -10x1 + e*x2 *2 = -2x2
Transcribed Image Text:3. Given the following Lyapunov candidate function, V = x"x and V = a" à + à"x = a" (A(t) + A" (t))æ < -Ax"x < -AV -Amazt the system is For the following system, show that for all t > 0 0 < x"x = V (t) < V(0)e¬^ asymptotically stable at the origin. *1 = -10x1 + e*x2 *2 = -2x2
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