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Q7.6-28E

Expert-verifiedFound in: Page 267

Book edition
5th

Author(s)
David C. Lay, Steven R. Lay and Judi J. McDonald

Pages
483 pages

ISBN
978-03219822384

**Consider an invertible ****n × n**** matrix A such that the zero state is a stable equilibrium of the dynamical system $\overrightarrow{\mathbf{x}}{\mathbf{(}}{\mathbf{t}}{\mathbf{+}}{\mathbf{1}}{\mathbf{)}}{\mathbf{=}}{\mathbf{A}}\overrightarrow{\mathbf{x}}{\mathbf{\left(}}{\mathbf{t}}{\mathbf{\right)}}$ ****What can you say about the stability of the systems**

** $\overrightarrow{\mathbf{x}}{\mathbf{(}}{\mathbf{t}}{\mathbf{+}}{\mathbf{1}}{\mathbf{)}}{\mathbf{=}}{\left(A-2{I}_{n}\right)}\overrightarrow{\mathbf{x}}{\mathbf{\left(}}{\mathbf{t}}{\mathbf{\right)}}$**

The given value is unstable

Eigenvalues can be used to determine whether a fixed point (also known as an equilibrium point) is stable or unstable.

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