# ROBUST HYBRID CONTROL SYSTEMS

Topic: All

4 juillet 2006, salle L106, École des Mines de Paris à Paris

13h30 Andy TEEL, Department of Electrical and Computer Engineering, University of California at Santa Barbara.

This talk will focus on robustness issues in hybrid control for nonlinear systems. By a hybrid controller we mean a dynamical system for which the state can evolve continuously and/or make (discontinuous) jumps, depending on where the state and its measurement are. We will motivate, from a robustness point of view, a solution concept for hybrid systems where solutions are defined on hybrid time domains and non-unique solutions are typical, especially in hybrid control systems that employ decision making. We will work with certain basic assumptions on the system data used to define the hybrid system. When the data does not satisfy these assumptions, we will motivate the concept of generalized solutions. These are solutions to the ``closest'' data set that satisfies the basic assumptions. We will show that, when generalized solutions are considered, many of the classical robust stability theory results from differential equations can be established for hybrid systems. These include results on robust uniform asymptotic stability, converse Lyapunov theorems, an invariance principle like LaSalle's, a theory of robust simulation, and a singular perturbation theory. The ideas in this talk will be illustrated by examples.

13h30 Andy TEEL, Department of Electrical and Computer Engineering, University of California at Santa Barbara.

This talk will focus on robustness issues in hybrid control for nonlinear systems. By a hybrid controller we mean a dynamical system for which the state can evolve continuously and/or make (discontinuous) jumps, depending on where the state and its measurement are. We will motivate, from a robustness point of view, a solution concept for hybrid systems where solutions are defined on hybrid time domains and non-unique solutions are typical, especially in hybrid control systems that employ decision making. We will work with certain basic assumptions on the system data used to define the hybrid system. When the data does not satisfy these assumptions, we will motivate the concept of generalized solutions. These are solutions to the ``closest'' data set that satisfies the basic assumptions. We will show that, when generalized solutions are considered, many of the classical robust stability theory results from differential equations can be established for hybrid systems. These include results on robust uniform asymptotic stability, converse Lyapunov theorems, an invariance principle like LaSalle's, a theory of robust simulation, and a singular perturbation theory. The ideas in this talk will be illustrated by examples.