Infinite horizon quadratic control of linear singularly perturbed systems with small state delays: an asymptotic solution of Riccati-type equations

2006 ◽  
Vol 24 (4) ◽  
pp. 435-459 ◽  
Author(s):  
V. Y. Glizer
Keyword(s):  
Asymptotic Solution ◽  
Infinite Horizon ◽  
Singularly Perturbed ◽  
Singularly Perturbed Systems ◽  
Small State ◽  
State Delays ◽  
Perturbed Systems

scholarly journals Regularization Method for Nonlinear Singularly Perturbed Systems of Fractional Order

2018 ◽  
Vol 6 (3) ◽  
Author(s):  
Burkhan Kalimbetov ◽  
Riskeldy Turgunbaev
Keyword(s):  
Asymptotic Solution ◽  
Fractional Order ◽  
Regularization Method ◽  
Differential Forms ◽  
Approximate Solutions ◽  
Singularly Perturbed ◽  
Singularly Perturbed Systems ◽  
Weakly Nonlinear ◽  
Mathematical System ◽  
Perturbed Systems

The paper is devoted to construction of an asymptotic solution of a weakly nonlinear singularly perturbed differential system of fractional order. To construct the asymptotic solution we use ideas of normal differential forms method of V.F. Safonov. In the environment of the computer mathematical system Maple, approximate solutions are calculated, and corresponding solution schedules for various values of a small parameter are constructed.

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