Nonlinear Control system

Abstract

Automatic control systems are pervasive across many industrial sectors, including aerospace, aeronautics, automotive engineering, and process engineering. Developing tools for analyzing and designing control and observation laws is essential to ensure the proper functioning of these systems. Initially, such tools were designed for linear or linearized systems. However, approximating a system by its tangent linearization often proves insufficient—or even unsuitable—for most real-world systems, which exhibit inherently nonlinear behavior on a global scale. Therefore, it is crucial to consider, study, and develop dedicated tools for nonlinear systems. The aim of this course is to highlight the fundamental differences between linear and nonlinear systems, to present methods for analyzing nonlinear systems, and to introduce selected techniques for synthesizing control laws for such systems. To facilitate understanding, this course material introduces a collection of classical results, often scattered across various references. The purpose is not to provide an exhaustive review of all research in the field, but rather to emphasize the key contributions that form the foundational basis of nonlinear systems theory. These results are particularly useful as a starting point for master’s and postgraduate students seeking to explore this subject. Notably, the course draws inspiration from well-established works such as "Nonlinear Systems" by H. Khalil and "Nonlinear Systems Analysis" by J.-J. Slotine. This approach, which I have successfully applied for several years, offers a good balance: it saves time while encouraging student engagement by having them complete the missing parts during the course. This also fosters better interaction in class. As with any work, there is always room for improvement. I welcome feedback, corrections, or suggestions from readers. Please feel free to reach out to the email address provided on the cover page. Thank you in advance for your contributions.