Summary of the seminar:

Lyapunov's direct method is widely regarded as a powerful method to study (Lyapunov) stability of dynamical systems. Originally introduced for nonlinear autonomous differential equations, modern extensions include discontinuous systems, systems with jumps, systems with impulsive dynamics, time delays, etc. This course focusses on the study of systems with smooth dynamics since in a number of engineering control problems "basic" nonlinear control theory may be used to design stabilizing controllers. However, in control of physical systems (robots, marine vehicles, motors, etc) realistic scenarios impose uncertainties in the parameters and the impossibility of measuring the whole system's state. Solving such problems through systematic Lyapunov-based design may rapidly become intractable only because of our inability to find a (control) Lyapunov function. Therefore, standard Lyapunov theory for nonlinear time-varying systems, as developed by Barbashin and Krasovskii in the 1950s may rapidly appear frustrating since rendering our analysis inconclusive.

In this course we study Lyapunov stability without a (strict) Lyapunov function via alternative methods which involve:

invariance principles and tools from real analysis (Barbalat);
integrability conditions (Panteley et al);
differential conditions with more than one auxiliary function (Matrosov);
feedback and cascade-interconnected systems (Panteley, Lora);.

The lectures are intended for PhD students and researchers willing to strengthen their knowledge in stability analysis of complex nonlinear systems. It is composed of 21 1-hr lessons

Short bio:

A. Loría was born in Mexico City, in 1969. He got the BSc degree in Electronic Systems Engineering from the "Monterrey Institute of Technological and Higher Studies (ITESM) in 1991. He got the DEA (~MSc) and PhD in Control Engineering degrees from the "University of Technology of Compiègne" in 1993 and 1996 respectively, both under the supervision of Romeo Ortega. From December 1996 till May 1997 he was a research fellow of the Department of Applied Mathematics at the University of Twente. From May through December 1997 he was a research fellow of the Department of Engineering Cybernetics at the Norwegian Institute of Science and Technology. From January through December 1998, he was an associate research engineer of the Center for Control Engineering and Computation, under the sponsorship of Prof. Petar Kokotovic and Prof. Andrew Teel. A. Loría occupies a permanent Research position at the French National Council of Scientific Research (CNRS) since 1999 (Senior Researcher since 2007) and is with Laboratoire de Signaux et Systèmes since 2001.