Lecture will be divided into three parts, following the below classification: Function -> Dynamic Systems -> Control Systems

Normal (cannonical) form is a representative object of a class.

Three pillars of nonlinear analysis:

1. Inverse function theorem.
2. Existence and Uniqueness of Solution of ODE
3. Frobenius Theorem on Integrability of Distributions

• Carthorse of Nonlinear Analysis: Fixed Point Theorem

Functions

Fig 1