Asymptotic Stability Equals Exponential Stability, and Iss Equals Nite Energy Gain|if You Twist Your Eyes
نویسندگان
چکیده
In this paper we show that uniformly global asymptotic stability for a family of ordinary diierential equations is equivalent to uniformly global exponential stability under a suitable nonlinear change of variables. The same is shown for input-to-state stability and input-to-state exponential stability, and for input-to-state exponential stability and a nonlinear H 1 estimate.
منابع مشابه
Asymptotic stability equals exponential stability, and ISS equals finite energy gain—if you twist your eyes
In this paper we show that uniformly global asymptotic stability for a family of ordinary differential equations is equivalent to uniformly global exponential stability under a suitable nonlinear change of variables. The same is shown for input-to-state stability and input-to-state exponential stability, and for input-to-state exponential stability and a nonlinear H∞ estimate.
متن کاملOn the Equivalence between Asymptotic and Exponential Stability, and between Iss and Nite H 1 Gain
We show that uniformly global asymptotic stability and input-to-state stability for a family of ordinary diierential equations are equivalent to uniformly global exponential stability and a nonlinear H1 estimate, respectively , under suitable nonlinear changes of variables.
متن کاملGlobal Asymptotic and Exponential Stability of Tri-Cell Networks with Different Time Delays
In this paper, a bidirectional ring network with three cells and different time delays is presented. To propose this model which is a good extension of three-unit neural networks, coupled cell network theory and neural network theory are applied. In this model, every cell has self-connections without delay but different time delays are assumed in other connections. A suitable Lyapun...
متن کاملNotions of Input to Output Stability
This paper deals with concepts of output stability. Inspired in part by regulator theory, several variants are considered, which diier from each other in the requirements imposed upon transient behavior. The main results provide a comparison among the various notions, all of which specialize to input to state stability (iss) when the output equals the complete state.
متن کامل2 J ul 1 99 9 Notions of Input to Output Stability
This paper deals with concepts of output stability. Inspired in part by regulator theory, several variants are considered, which differ from each other in the requirements imposed upon transient behavior. The main results provide a comparison among the various notions, all of which specialize to input to state stability (iss) when the output equals the complete state.
متن کامل