On the Equivalence between Asymptotic and Exponential Stability, and between Iss and Nite H 1 Gain
نویسندگان
چکیده
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.
منابع مشابه
Asymptotic Stability Equals Exponential Stability, and Iss Equals Nite Energy Gain|if You Twist Your Eyes
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.
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