40.13 LYAPUNOV'S LINEARIZATION METHOD

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This method addresses the local stability of a non-linear system when linearized.

In essense it validated the use of linear control systems on non-linear systems.

Lyapunov's stability theorem focuses on the stablilty (Eigenvalues) of matrix A at a given point.

- The system is asymptotically stable at the equillibrium point if all of the Eigenvalues of A are in the left hand complex plane.

- The system is unstable as the equillibrium point if the matrix A is unstable, with points in the right hand side of the complex plane.

- If all of the Eigenvalues are in the left hand plane, except for one or more on the complex axis, then the system is marginally stable, and the linearization may be stable or unstable.