Initial conditions for reduced-order models of nonlinear singularly perturbed systems

2002 ◽  
Author(s):  
K.W. Cheung ◽  
J.H. Chow
Keyword(s):  
Initial Conditions ◽  
Singularly Perturbed ◽  
Reduced Order Models ◽  
Singularly Perturbed Systems ◽  
Reduced Order ◽  
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.

Robust Stabilization for a Class of Nonlinear Singularly Perturbed Systems

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
R. Amjadifard ◽  
M. T. H. Beheshti ◽  
M. J. Yazdanpanah
Keyword(s):  
Robust Stabilization ◽  
Singularly Perturbed ◽  
Disturbance Attenuation ◽  
Order System ◽  
Singularly Perturbed Systems ◽  
Existence Of A Solution ◽  
New Approach ◽  
Reduced Order ◽  
Main System ◽  
Perturbed Systems

In this paper, the problem of disturbance attenuation with internal stability for a class of nonlinear singularly perturbed systems via nonlinear H∞ approach is studied. It is shown through a useful theorem that under appropriate assumptions, the problem of disturbance attenuation for the main system may be related to the problem of disturbance attenuation for the reduced-order system. This is carried out by a new approach in which we use the quasi-steady state of fast variables. Therefore, the problem of existence of a positive definite solution for the Hamilton–Jacobi–Isaacs (HJI) inequality related to the main system leads to the problem of existence of a solution of a simpler HJI inequality related to the reduced-order system.

Sign in / Sign up

Export Citation Format

Share Document