Differential-algebraic equations and nonstandard singularly perturbed control systems

1990 ◽  
Author(s):  
N.H. McClamroch ◽  
H. Krishnan
Keyword(s):  
Control Systems ◽  
Differential Algebraic Equations ◽  
Singularly Perturbed ◽  
Algebraic Equations

scholarly journals Bifurcation in Singularity Parameterized ODEs

2016 ◽  
Vol 12 (1) ◽  
pp. 5808-5816
Author(s):  
Kamal H Yasir ◽  
Zahraa A Mutar
Keyword(s):  
Sufficient Conditions ◽  
Differential Algebraic Equations ◽  
Transcritical Bifurcation ◽  
Singularly Perturbed ◽  
Algebraic Equations ◽  
Parameter Approach ◽  
New System

In this paper we will study differential algebraic equations (DAEs) through studying singularly perturbed ODEs. That's the ODEs will be transformed to an DAEs when the perturbed parameter approach to 0. This will permit us to apply the classicalbifurcation theory of ODEs for the new system (DAEs). So we will show by giving theorems, sufficient conditions for fold, pitchfork and transcritical bifurcation to be occurred in (DAEs). An illustrative example is given.

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