Asymptotic solution of a singularly perturbed nonlinear state regulator problem

1995 ◽  
Vol 16 (6) ◽  
pp. 515-520
Author(s):  
Lin surong ◽  
Lin Zongchi
Keyword(s):  
Asymptotic Solution ◽  
Singularly Perturbed ◽  
Regulator Problem ◽  
State Regulator ◽  
Nonlinear State

The Singularly Perturbed Linear State Regulator Problem. II

1975 ◽  
Vol 13 (2) ◽  
pp. 327-337 ◽  
Author(s):  
R. E. O’Malley ◽  
C. F. Kung
Keyword(s):  
Singularly Perturbed ◽  
Regulator Problem ◽  
State Regulator ◽  
Linear State

The Singularly Perturbed Linear State Regulator Problem

1972 ◽  
Vol 10 (3) ◽  
pp. 399-413 ◽  
Author(s):  
R. E. O’Malley, Jr.
Keyword(s):  
Singularly Perturbed ◽  
Regulator Problem ◽  
State Regulator ◽  
Linear State

scholarly journals Regularized Solution of Singularly Perturbed Cauchy Problem in the Presence of Rational “Simple” Turning Point in Two-Dimensional Case

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 124 ◽  
Author(s):  
Alexander Eliseev ◽  
Tatjana Ratnikova
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Solution ◽  
Regularization Method ◽  
Turning Point ◽  
Singularly Perturbed ◽  
Dimensional Case ◽  
Singularly Perturbed Problem ◽  
Two Dimensional ◽  
Limit Operator ◽  
Regularized Solution

By Lomov’s S.A. regularization method, we constructed an asymptotic solution of the singularly perturbed Cauchy problem in a two-dimensional case in the case of violation of stability conditions of the limit-operator spectrum. In particular, the problem with a ”simple” turning point was considered, i.e., one eigenvalue vanishes for t = 0 and has the form t m / n a ( t ) (limit operator is discretely irreversible). The regularization method allows us to construct an asymptotic solution that is uniform over the entire segment [ 0 , T ] , and under additional conditions on the parameters of the singularly perturbed problem and its right-hand side, the exact solution.

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