september 23

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\def\Field{\mathbb{F}}
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Global asymptotic stability for LTI.

Equivalent to local stability.

Hurwitz operators. Multiple eigenvalues and Jordan normal forms.

Lyapunov’s direct method

Positive definite functions.

Lyapunov functions, definition.

Lyapunov’s theorem.

Convenient Lyapunov functions: homogeneous ones.

Strict homogeneous Lyapunov function for a linear system remains one after a perturbation of the system.

Examples.

Good homogeneous functions: quadratic forms.

Quadratic forms

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