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Consider the system = (41%) (22) + (1) * น in which a is a constant (a) Determine the condition under which the system is controllable (b) For a 1 (i) Show that et4 = (cos(t)) sin(t)) cos(t)) (Hint: You may note that A4 = 1, A4k+1 = A, A4k+2 = −I, A4+3 = -A for all k > 0 and determine the MacLaurin series expansion of cos(t) and sin(t)) To (ii) Write the integral formula for the solution X (t) in terms of X (0) = X₁ = and u. Yo (ii) Extract a separate formula for each component of X(t) = ((0)

Consider the system = (41%) (22) + (1) * น in which a is a constant (a) Determine the condition under which the system is controllable (b) For a 1 (i) Show that et4 = (cos(t)) sin(t)) cos(t)) (Hint: You may note that A4 = 1, A4k+1 = A, A4k+2 = −I, A4+3 = -A for all k > 0 and determine the MacLaurin series expansion of cos(t) and sin(t)) To (ii) Write the integral formula for the solution X (t) in terms of X (0) = X₁ = and u. Yo (ii) Extract a separate formula for each component of X(t) = ((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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Consider the system = (41%) (22) + (1) * น in which a is a constant (a) Determine the condition under which the system is controllable (b) For a 1 (i) Show that et4 = (cos(t)) sin(t)) cos(t)) (Hint: You may note that A4 = 1, A4k+1 = A, A4k+2 = −I, A4+3 = -A for all k > 0 and determine the MacLaurin series expansion of cos(t) and sin(t)) To (ii) Write the integral formula for the solution X (t) in terms of X (0) = X₁ = and u. Yo (ii) Extract a separate formula for each component of X(t) = ((0)
Transcribed Image Text:Consider the system = (41%) (22) + (1) * น in which a is a constant (a) Determine the condition under which the system is controllable (b) For a 1 (i) Show that et4 = (cos(t)) sin(t)) cos(t)) (Hint: You may note that A4 = 1, A4k+1 = A, A4k+2 = −I, A4+3 = -A for all k > 0 and determine the MacLaurin series expansion of cos(t) and sin(t)) To (ii) Write the integral formula for the solution X (t) in terms of X (0) = X₁ = and u. Yo (ii) Extract a separate formula for each component of X(t) = ((0)
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