Title :
Dissipativity theory and stability of feedback interconnections for hybrid dynamical systems
Author :
Haddad, Wassim M. ; Chellaboina, VijaySekhar
Author_Institution :
Sch. of Aerosp. Eng., Georgia Inst. of Technol., Atlanta, GA, USA
Abstract :
We develop a unified framework for a general class of dynamical 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 and impulsive dynamical systems as special cases. Furthermore, we generalize dissipativity theory to left-continuous dynamical systems. Finally, the generalized dissipativity notions are used to develop general stability criteria for feedback interconnections of left-continuous systems. These results generalize the positivity and small gain theorems to the case of left-continuous, hybrid, and impulsive dynamical systems
Keywords :
Lyapunov methods; asymptotic stability; closed loop systems; feedback; stability criteria; dissipativity theory; feedback interconnections; hybrid dynamical systems; impulsive dynamical systems; left-continuous dynamical systems; left-continuous flows; positivity; small gain theorem; Aerodynamics; Aerospace engineering; Control systems; Decision making; Differential equations; Feedback; Lighting control; Nonlinear control systems; Stability; Vehicle dynamics;
Conference_Titel :
American Control Conference, 2000. Proceedings of the 2000
Conference_Location :
Chicago, IL
Print_ISBN :
0-7803-5519-9
DOI :
10.1109/ACC.2000.878694
