Stabilizability of a class of linear singularly perturbed systems via output feedback

In this article, stability of a class of linear singularly perturbed systems via output feedback is investigated. It is shown that the whole closed-loop systems are either exponentially stable as the perturbed parameter ε goes to zero or are not stabilizable by any controller. Moreover, in order to expand the upper range of the perturbation parameter ε, the switched output feedback controller is designed. It is shown that, when stabilization is possible, the whole closed-loop singularly perturbed systems are exponentially stable as the feedback gain can be chosen to take on no more than two values throughout the entire state-space for any given perturbation parameter ε.