In this paper, the problem of disturbance attenuation with internal stability for a class of nonlinear singularly perturbed systems via nonlinear 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.
Robust Stabilization for a Class of Nonlinear Singularly Perturbed Systems
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Amjadifard, R., Beheshti, M. T. H., and Yazdanpanah, M. J. (July 27, 2011). "Robust Stabilization for a Class of Nonlinear Singularly Perturbed Systems." ASME. J. Dyn. Sys., Meas., Control. September 2011; 133(5): 051004. https://doi.org/10.1115/1.4003383
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