2. Suppose that the pair (A, C) is detectable. Show that if the Lyapunov matrix equation ATP + PA = -CTC has a symmetric positive definite solution P, then A has negative real-part eigenvalues.

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Chapter7: Eigenvalues And Eigenvectors
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2. Suppose that the pair (A, C) is detectable. Show that if the Lyapunov
matrix equation ATP + PA = -CTC has a symmetric positive definite
solution P, then A has negative real-part eigenvalues.
Transcribed Image Text:2. Suppose that the pair (A, C) is detectable. Show that if the Lyapunov matrix equation ATP + PA = -CTC has a symmetric positive definite solution P, then A has negative real-part eigenvalues.
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