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Strong stability and the Cayley transform
Author(s) -
Halikias George
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2976
Subject(s) - mathematics , stability (learning theory) , domain (mathematical analysis) , transformation (genetics) , exponential stability , state space , pure mathematics , lyapunov function , state (computer science) , space (punctuation) , mathematical analysis , algebra over a field , computer science , nonlinear system , algorithm , biochemistry , chemistry , physics , statistics , quantum mechanics , machine learning , gene , operating system
The general notion of ‘strong’ stability for internal autonomous system descriptions has been recently introduced for continuous and discrete‐time systems. This is a stronger notion of stability compared with alternative definitions (asymptotic, Lyapunov), which prohibits systems described by natural coordinates to have overshooting responses, for arbitrary initial conditions in state space. The paper reviews three refined notions of strong stability, along with the necessary and sufficient conditions corresponding to each notion. Using the Cayley transformation, it is shown that the notions in the two domains are essentially equivalent and that the strong stability conditions can be transformed from one domain to the other in a straightforward way. Copyright © 2013 John Wiley & Sons, Ltd.