Perturbed Linear System
Not what you're looking for? Search our solutions OR ask your own Custom question.
Consider the perturbed linear system
x' = (A + eB(t))x, x is an element of R^n,
where A is a constant matrix, B is a bounded continuous matrix valued function, and e is a small parameter. Assume that all eigenvalues of A have non-zero real part.
1) Show that the only bounded solution of the system is 0.
2) If A has an eigenvalue with zero real part, then is the above still true?
© BrainMass Inc. brainmass.com March 6, 2023, 12:49 pm ad1c9bdddfhttps://brainmass.com/math/linear-algebra/perturbed-linear-system-21792
Solution Summary
This is a proof regarding the bounded solution of a perturbed linear system. The solution is enclosed within a Word document.
$2.49