Dynamic output feedback control of nonlinear singularly perturbed systems

In this paper, the stabilization problem of two classes of nonlinear singularly perturbed systems via dynamic output feedback is investigated. First, we consider the nonlinear singularly perturbed systems in which the nonlinearities are continuously differentiable. The theoretical result demonstrates that, using the factorization approach, the dynamic output feedback controller designed for the reduced-order model of the linearized system is a stabilizing compensator for the original nonlinear singularly perturbed system, provided that ε is sufficiently small. Second, the nonlinear singularly perturbed systems in which the nonlinearities are not necessarily continuously differentiable but satisfy the global Lipschtz condition are examined. Combining the dynamic output feedback controller that stabilizes the reduced-order model of the linear part of the nonlinear singularly perturbed system with the quasi-stability result of Persidskii, a two-step compensating scheme is proposed to stabilize the original nonlinear singularly perturbed system under consideration for a sufficiently small ε.