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A homogeneity property of discrete‐time systems: Stability and convergence rates
Author(s) -
Sanchez Tonametl,
Efimov Denis,
Polyakov Andrey,
Moreno Jaime A.,
Perruquetti Wilfrid
Publication year - 2019
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4497
Subject(s) - homogeneity (statistics) , mathematics , lyapunov function , scaling , homogeneous , discrete time and continuous time , dilation (metric space) , property (philosophy) , mathematical analysis , control theory (sociology) , geometry , computer science , nonlinear system , physics , statistics , combinatorics , philosophy , control (management) , epistemology , quantum mechanics , artificial intelligence
Summary A new definition of homogeneity for discrete‐time systems is introduced. As in the continuous‐time case, the property can be verified algebraically in the transition map of the system, and it implies that a dilation of the initial conditions leads to a scaling of the trajectory. Stability properties and convergence rates of the system's solutions can be established by considering only the homogeneity degree. The existence of homogeneous Lyapunov and Lyapunov‐like functions is proven.