Uniform Asymptotic Stability of Evolutionary Processes in a Banach Space

1972 ◽  
Vol 3 (3) ◽  
pp. 428-445 ◽  
Author(s):  
Richard Datko
Keyword(s):  
Banach Space ◽  
Asymptotic Stability ◽  
Uniform Asymptotic Stability ◽  
Evolutionary Processes

Uniform asymptotic stability, an initial treatment

2012 ◽  
Author(s):  
Rafal Goebel ◽  
Ricardo G. Sanfelice ◽  
Andrew R. Teel
Keyword(s):  
Asymptotic Stability ◽  
Equilibrium Point ◽  
Single Point ◽  
Fundamental Property ◽  
Uniform Asymptotic Stability ◽  
Closed Set ◽  
Long Term Trends ◽  
Engineered Systems

This chapter focuses on the uniform asymptotic stability of a closed set. Asymptotic stability is a fundamental property of dynamical systems—one that is usually desired in natural and engineered systems. It provides qualitative information about solutions, especially a characterization of the solutions' long-term trends. The asymptotic stability of a closed set, rather than of an equilibrium point, is significant since the solutions of a hybrid system often do not settle down to an equilibrium point. Furthermore, the asymptotic stability of an equilibrium point is a special case of asymptotic stability of a closed set. Namely, an equilibrium point is a closed set containing a single point.

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