Stability of nonlinear systems
The objective of this course is to provide tools for the analysis of nonlinear dynamical systems modelled by ordinary differential equations. These include engineering systems, such as robotic, automotive, and aerospace systems, but also biological and socio-economical systems. A key aspect of these equations is that their nonlinear nature usually prevents the calculation of an explicit solution. Furthermore, the frequency methods commonly used for linear systems do not apply in this context. We rely on stability theory to assess the qualitative behavior of dynamical systems. This course introduces specific stability notions and analysis tools tailored for nonlinear systems. Furthermore, beyond stability, these tools also enable to study the systems performance, robustness to disturbances, and interconnections.
References
- Nonlinear Systems, Hassan Khalil, Pearson (3rd ed) 2001.
- Nonlinear Systems Analysis, M. Vidyasagar, SIAM Classics in Applied Mathematics (2nd edition), 2002.
- Ordinary Differential Equations, Part II, N. Rouche and J. Mawhin (Translation from : Équations Différentielles Ordinaires Tome II: Stabilité et Solutions Périodiques. Rouche, Nicolas, and Jean Mawhin. Paris: Masson, 1973).