On guaranteed global exponential stability of polynomial singularly perturbed control systems

2006 ◽  
Author(s):  
Hajer Bouzaouache ◽  
Naceur Benhadj Braiek
Keyword(s):  
Exponential Stability ◽  
Control Systems ◽  
Global Exponential Stability ◽  
Singularly Perturbed

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.

Control Systems for Ultra-High Rise Elevators1

1998 ◽  
Vol 123 (4) ◽  
pp. 687-690
Author(s):  
S. R. Venkatesh ◽  
Y. M. Cho
Keyword(s):  
Exponential Stability ◽  
Control Systems ◽  
Global Exponential Stability ◽  
Control Design ◽  
Vertical Motion ◽  
Lumped Parameter Model ◽  
Performance Tests ◽  
High Rise ◽  
Lumped Parameter ◽  
Wear And Tear

We present a scalable and tunable control design for controlling elevator vertical motion for ultra high-rise buildings. Scalability is desirable to enable customization to any hoistway while tunability enables periodic adjustments to normal wear and tear. We accomplish these objectives by first validating a scalable lumped parameter model that is based on a few prominent features in the vertical dynamics. A tunable controller based only on these features is developed and through simulations we show that the controller meets a set of standardized elevator performance tests while maintaining global exponential stability.

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