An observer‐based output feedback stabilizing controller for singularly perturbed systems

Summary This paper studies the dynamic output feedback stabilization of singularly perturbed systems. A new ‐free output feedback stabilizing controller based on a slow state observer is designed for singularly perturbed systems. Compared with existing dynamic ‐free output feedback controller designs, the proposed stabilizing controller can estimate the slow state in the presence of unstable fast modes. Sufficient conditions are given to guarantee the asymptotical stability of the closed‐loop system. The gain matrix of the observer‐based controller can be obtained by solving a general eigenvalue problem, and at the same time, an upper bound of parameter that guarantees the stability of the closed‐loop system is obtained. Simulation results show that the proposed controller design method is effective.