On the Exponential Stability of Singularly Perturbed Systems

1992 ◽  
Vol 30 (6) ◽  
pp. 1338-1360 ◽  
Author(s):  
Martin Corless ◽  
Luigi Glielmo
Keyword(s):  
Exponential Stability ◽  
Singularly Perturbed ◽  
Singularly Perturbed Systems ◽  
Perturbed Systems

scholarly journals On Guaranteed Global Exponential Stability Of Polynomial Singularly Perturbed Control Systems

2006 ◽  
Vol 1 (4) ◽  
pp. 21 ◽  
Author(s):  
Hajer Bouzaouache ◽  
Naceur Benhadj Braiek
Keyword(s):  
Exponential Stability ◽  
Global Exponential Stability ◽  
Integral Manifold ◽  
Singularly Perturbed ◽  
Linear Matrix ◽  
Singularly Perturbed Systems ◽  
Closed Loop System ◽  
Reduced Order ◽  
Perturbed Systems ◽  
The Stability

The problem of global exponential stability for a class of nonlinear singularly perturbed systems is examined in this paper. The stability analysis is based on the use of basic results of integral manifold of nonlinear singularly perturbed systems, the composite Lyapunov method and the notations and properties of Tensoriel algebra. Some of the derived results are presented as linear matrix inequalities (LMIs) feasibility tests. Moreover, we pointed out that if the global exponential stability of the reduced order subsystem is established this is equivalent to guarantee the global exponential stability of the original high order closed loop system. An upper bound e1 of the small parameter e , can also be determined up to which established stability conditions via LMI’s are maintained verified. A numerical example is given to illustrate the proposed approach.

Practical exponential stability and closeness of solutions for singularly perturbed systems via averaging

Automatica ◽  
2021 ◽  
Vol 126 ◽  
pp. 109449
Author(s):  
Mohammad Deghat ◽  
Saeed Ahmadizadeh ◽  
Dragan Nešić ◽  
Chris Manzie
Keyword(s):  
Exponential Stability ◽  
Singularly Perturbed ◽  
Singularly Perturbed Systems ◽  
Perturbed Systems
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