Fundamentals of Nonlinear Control

This course is offered to master and PhD students by the Graduate Program in Electrical Engineering at UFMG.

The classes were designed to follow closely the textbook “Nonlinear Systems”, by Hassan K. Khalil, 3rd Edition, according to this set of Lecture Notes made available by the author.

Complementary Material

• Fundamentos de Controle Não Linear – Introdução e Conceitos Básicos (in Portuguese)
• Fundamentos de Controle Não Linear: Conceitos Matemáticos Importantes (in Portuguese)
• O Método da Função Descritiva (in Portuguese)
• Teoria de Estabilidade de Lyapunov (in Portuguese)

A sotware to easily draw Phase Portraits (by Prof. John C. Polking, at the Department of Mathematics of the Rice University)

• dfield and pplane – Java versions
• dfield and pplane – MATLAB versions

Some interesting books to advance your knowledge in Mathematics:

1. Some Modern Mathematics for Physicists and Other Outsiders: An Introduction to Algebra, Topology, and Functional Analysis – Volume 1, by Paul Roman (1975)

   In this book I have found a warming introduction to mathematics for those that came from other technical areas like Engineering. By reading this book, one begins to understand a mathematician’s mindset.
2. How to Think Like a Mathematician: A Companion to Undergraduate Mathematics, by Kevin Houston (2009)

   A very gentle introduction to mathematical logic. Easy to read and enjoyable.

    

3. What Is Mathematics?: An Elementary Approach to Ideas and Methods, by Richard Courant,‎ Ian Stewart,‎ Herbert Robbins (2016)

   From the Introduction:

   “Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science.

   Without doubt, all mathematical development has its psychological roots in more or less practical requirements. But once started under the pressure of necessary applications, it inevitably gains momentum in it-itself and transcends the confines of immediate utility. This trend from applied to theoretical science appears in ancient history as well as in many contributions to modern mathematics by engineers and physicists.”