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Let us consider a continuous-time system represented by the following differential equation : 5+ 3a du 5 - 3a -231 u(0) : dt 10 – 3a -4a 232 -4a 10 + 3a B2

Let us consider a continuous-time system represented by the following differential equation : 5+ 3a du 5 - 3a -231 u(0) : dt 10 – 3a -4a 232 -4a 10 + 3a B2

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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Determine the eigenvalues of matrix A! Express your answer in terms of a! Determine also the corresponding eigenvectors of matrix A! Determine the system's output as a function of time u(t) for this system! Express your answer in terms of a! What should be the value of a so that the system is stable (u(t → -) = 0) for the aforementioned initial condition? Is it possible to adjust the value of a so that this system is stable for every initial condition? Please explain your reason! b1 =1 b2= 7
Transcribed Image Text:Determine the eigenvalues of matrix A! Express your answer in terms of a! Determine also the corresponding eigenvectors of matrix A! Determine the system's output as a function of time u(t) for this system! Express your answer in terms of a! What should be the value of a so that the system is stable (u(t → -) = 0) for the aforementioned initial condition? Is it possible to adjust the value of a so that this system is stable for every initial condition? Please explain your reason! b1 =1 b2= 7
Let us consider a continuous-time system represented by the following differential equation : 5+ 3a B1 du 40 5 - 3a -231 u(0) = dt 10 – 3a -4a 232 -4a 10 + 3a B2
Transcribed Image Text:Let us consider a continuous-time system represented by the following differential equation : 5+ 3a B1 du 40 5 - 3a -231 u(0) = dt 10 – 3a -4a 232 -4a 10 + 3a B2
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