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Unformatted text preview: ( x, y, z ) = ( ky ,y , ) , Convergence of y ( t ) to y is trivial (recall that y ( t ) = y ), so the only thing left to show is that the x and z components converge. The remaining equations are: x =-ky x + z = ky x-z * MAP 4484 / 5489; Instructor: Patrick De Leenheer. 1 In matrix form : p x z P = p-ky ky- Pp x z P + p P By the note below, and since the matrix above has two negative eigenvalues-ky and- , we conclude that solutions of the last system converge to ( /ky ,y ,/ ). (Note: You may use the fact that if X = AX + B is a non-homogeneous linear system of arbitrary dimension n which is such that all eigenvalues of A are in the open left half plane, then all solutions converge to the steady state X =-A-1 B .) 2...
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This note was uploaded on 09/12/2011 for the course MAP 4305 taught by Professor Deleenheer during the Summer '06 term at University of Florida.
- Summer '06