A Unified Framework for Analysis and Synthesis of Hybrid Dynamical Systems
by
Wassim M. Haddad
Georgia Institute of Technology

In this work we develop a unified dynamical systems framework for a general class of systems possessing left-continuous flows; that is, left continuous dynamical systems. These systems are shown to generalize virtually all existing notions of dynamical systems and include hybrid, impulsive, and switching systems as special cases. Furthermore, we generalize dissipativity, passivity, and nonexpansivity (nonlinear Hoo) theory to left-continuous dynamical systems. Specifically, the classical concepts of system storage functions and supply rates are extended to left-continuous dynamical systems providing a generalized hybrid system energy interpretation in terms of stored energy, dissipated energy over the continuous-time system dynamics, and dissipated energy over the resetting events. Finally these results are used to develop general stability criteria for feedback control of hybrid systems. The proposed framework is used to design high-performance hybrid controllers for suppressing thermoacoustic oscillations in combustion chambers by efficiently dissipating modal system energy.

Date received: February 1, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cago-34.