Title :
On the equivalence between asymptotic and exponential stability, and between ISS and finite H∞ gain
Author :
Grüne, Lars ; Sontag, Eduardo D. ; Wirth, Fabian
Author_Institution :
Fachbereich Math., Frankfurt Univ., Germany
fDate :
6/21/1905 12:00:00 AM
Abstract :
We show that uniformly global asymptotic stability and input-to-state stability for a family of ordinary differential equations are equivalent to uniformly global exponential stability and a nonlinear H∞ estimate, respectively, under suitable nonlinear changes of variables
Keywords :
H∞ control; asymptotic stability; differential equations; nonlinear control systems; ISS; exponential stability; finite H∞ gain; input-to-state stability; nonlinear H∞ estimate; nonlinear changes of variables; ordinary differential equations; uniformly global asymptotic stability; uniformly global exponential stability; Asymptotic stability; Control theory; Differential equations; Level set; Linear systems; Linearization techniques; Lyapunov method; Mathematics; Nonlinear control systems; Nonlinear systems;
Conference_Titel :
Decision and Control, 1999. Proceedings of the 38th IEEE Conference on
Conference_Location :
Phoenix, AZ
Print_ISBN :
0-7803-5250-5
DOI :
10.1109/CDC.1999.830097
