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1. Consider the system X(t) = AX(t) where A = ( a) - (1) ª and a a constant. (a) For which values of a is the system controllable? (b) For a = 1, i. Calculate et Io ii. Write the integral formula for the solution X(t) in terms of X(0) = Xo = yo and B = and u.

1. Consider the system X(t) = AX(t) where A = ( a) - (1) ª and a a constant. (a) For which values of a is the system controllable? (b) For a = 1, i. Calculate et Io ii. Write the integral formula for the solution X(t) in terms of X(0) = Xo = yo and B = and u.

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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1. Consider the system X(t) = AX(t) where A = (82) and B = (a) For which values of a is the system controllable? (b) For a = 1, i. Calculate et ii. Write the integral formula for the solution X(t) in terms of X(0) = Xo = iii. Extract a separate formula for each component of X(t) = ((1))- and a a constant. Io Yo and u.
Transcribed Image Text:1. Consider the system X(t) = AX(t) where A = (82) and B = (a) For which values of a is the system controllable? (b) For a = 1, i. Calculate et ii. Write the integral formula for the solution X(t) in terms of X(0) = Xo = iii. Extract a separate formula for each component of X(t) = ((1))- and a a constant. Io Yo and u.
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