(b) Given the system of equations (7.6) on page 55 of the notes, let us write z = 1 - s. Now for constants ao and a₁, let us define the function L(z(t), i(t), r(t)) = aoz(t) + i(t) + a₁r(t). Write down sufficient conditions in terms of ao and a₁ in order that L(z(t), i(t), r(t)) be a Lyapunov function with respect to the origin point (z, i, r) = (0,0,0).
(b) Given the system of equations (7.6) on page 55 of the notes, let us write z = 1 - s. Now for constants ao and a₁, let us define the function L(z(t), i(t), r(t)) = aoz(t) + i(t) + a₁r(t). Write down sufficient conditions in terms of ao and a₁ in order that L(z(t), i(t), r(t)) be a Lyapunov function with respect to the origin point (z, i, r) = (0,0,0).
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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Transcribed Image Text:(b) Given the system of equations (7.6) on page 55 of the notes, let us write z = 1 - s.
Now for constants ao and a₁, let us define the function
L(z(t), i(t), r(t)) = a¸² (t) + i(t) + ªr(t).
Write down sufficient conditions in terms of ao and an in order that L(z(t), i(t), r(t)) be a
Lyapunov function with respect to the origin point (z, i, r) = (0,0,0).
Transcribed Image Text:5
dt
μ-Bsi-us
Bisit Hệ
102
25 LT.
(7.6)
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