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(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
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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(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:(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).
5 dt μ-Bsi-us Bisit Hệ 102 25 LT. (7.6)
Transcribed Image Text:5 dt μ-Bsi-us Bisit Hệ 102 25 LT. (7.6)
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