Consider a linear system of the form d/dt x(t) = Ax. Next suppose there exists a...

Question

Question

Consider a linear system of the form d/dt x(t) = Ax. Next suppose there exists a positive definite solution to the matrix inequality:

A^TP + PA < 0
where M<0 means M is negative definite. Then prove that all eigenvalues of A have negative real part.

Answer 1

Answer #1

We have the following dynamical cystem, r(t) = Are. Lo And given, ATP+ PA <o. - > (2) Assuming it has the def?. soln & ATTACO Dear student,

This was a question of dynamical system, i have tried to solve it. Hope its helpful for you. Have written it stepwise.

Answer 2

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