New Results on Exponential Stability of Fractional Order Nonlinear Dynamic Systems

2016 ◽  
Vol 5 (4) ◽  
pp. 415-425 ◽  
Author(s):  
Tianzeng Li ◽  
Yu Wang ◽  
Yong Yang
Keyword(s):  
Exponential Stability ◽  
Fractional Order ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Systems

Equivalence of Lp Stability and Exponential Stability of Nonlinear Lipschitzian Semigroups

2012 ◽  
Vol 55 (4) ◽  
pp. 882-889
Author(s):  
Song Xueli ◽  
Peng Jigen
Keyword(s):  
Exponential Stability ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Sufficient Conditions ◽  
Nonlinear Dynamic Systems ◽  
Nonlinear Semigroup ◽  
Exponentially Stable ◽  
Lipschitzian Semigroup

AbstractLp stability and exponential stability are two important concepts for nonlinear dynamic systems. In this paper, we prove that a nonlinear exponentially bounded Lipschitzian semigroup is exponentially stable if and only if the semigroup is Lp stable for some p > 0. Based on the equivalence, we derive two sufficient conditions for exponential stability of the nonlinear semigroup. The results obtained extend and improve some existing ones.

Mittag–Leffler stability of fractional order nonlinear dynamic systems

Automatica ◽  
2009 ◽  
Vol 45 (8) ◽  
pp. 1965-1969 ◽  
Author(s):  
Yan Li ◽  
YangQuan Chen ◽  
Igor Podlubny
Keyword(s):  
Fractional Order ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Systems
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