On guaranteed global exponential stability of polynomial singularly perturbed control systems

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