ISSN:
1573-8698
Keywords:
34D15
;
34E15
;
34A60
;
93C73
;
93D20
;
49N99
;
Singular perturbation
;
differential inclusion
;
control systems
;
stability
Source:
Springer Online Journal Archives 1860-2000
Topics:
Electrical Engineering, Measurement and Control Technology
Notes:
Abstract We study the continuity properties of the bundle of solutions to a differential inclusion subject to a singular perturbation, i.e., with respect to a scalar parameter ɛ multiplying a part of the derivatives. We give conditions under which every solution of the singularly perturbed inclusion is close, in a certain sense and for a sufficiently small ɛ, to a solution of the degenerate inclusion obtained for ɛ=0. These conditions include both stability and structural requirements (the later having no counterpart in the case of a differential equation). The main result obtained generalizes the well-known Tikhonov theorem for singularly perturbed differential equations.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02463254
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