On Guaranteed Global Exponential Stability Of Polynomial Singularly Perturbed Control Systems | Zendy

Hajer Bouzaouache | Zendy; Naceur Benhadj Braïek | Zendy

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On Guaranteed Global Exponential Stability Of Polynomial Singularly Perturbed Control Systems

Author(s) -

Hajer Bouzaouache,

Naceur Benhadj Braïek

Publication year - 2006

Publication title -

international journal of computers communications and control

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.422

H-Index - 33

eISSN - 1841-9844

pISSN - 1841-9836

DOI - 10.15837/ijccc.2006.4.2303

Subject(s) - exponential stability , mathematics , nonlinear system , stability (learning theory) , polynomial , upper and lower bounds , lyapunov function , exponential function , control theory (sociology) , class (philosophy) , manifold (fluid mechanics) , mathematical analysis , control (management) , computer science , mechanical engineering , physics , quantum mechanics , machine learning , artificial intelligence , engineering

The problem of global exponential stability for a class of nonlinear singularly perturbed systems is examined in this paper. Our 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 epsiv of the small parameter epsiv , can also be determined up to which established stability conditions via LMI's are maintained verified

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