Abstract:

The stability of switched systems is a challenging problem of current interest. In this talk we will present some new results for the uniform global asymptotic stability of switched nonlinear systems with time/state-dependent switching constraints. These results are based on the existence of weak Lyapunov functions, i.e. positive definite functions for which the time derivative along the subsystems are only semidefinite negative. As a difference with most of the known criteria based on weak Lyapunov functions, our results do not assume any dwell-time condition, and consequently can be applied to switched systems with arbitrary fast switchings. The approach for obtaining the stability results consists of embedding the switched system into a control system whose outputs are related with the time derivatives of the Lyapunov functions, and then studying the behavior of the solutions of that control systems when its outputs are constrained to be identically zero. 

Bio:

José Luis Mancilla Aguilar received the Licenciado en Matemática degree (1994) and his Doctor’s degree in Mathematics (2001) from the Universidad Nacional de Buenos Aires (UBA), Argentina. From 1993 to 1995, he received a Research Fellowship from the Argentine Atomic Energy Commission (CNEA) in the area of nonlinear control. Since 1995, he has been with the Department of Mathematics of the Facultad de Ingeniería (UBA), where he is currently a part-time Associate Professor. Since 2005, Dr. Mancilla-Aguilar has held a Professor position at the Department of Mathematics of the Instituto Tecnológico de Buenos Aires (ITBA) and currently is the head of the Centro de Sistemas y Control (CeSyC). His research interests include hybrid systems and nonlinear control.

Watch the seminar on our YouTube channel: https://youtu.be/QQSHfjnLMbk