Reduced-Order Models for Feedback Stabilization of Linear Systems With a Singular Perturbation Model

The problem of output feedback stabilization of linear systems based on a reduced-order model is addressed in this paper. New reduced-order models are proposed for the output feedback design of linear systems with a singular perturbation model. An output feedback controller with a zero steady-state gain matrix is proposed for stabilizing this kind of system. It is shown that with the proposed controller the reduced-order model based feedback design can guarantee the actual closed-loop stability for the sufficiently small perturbation parameter. This approach can overcome the difficulties in the existing design method using the so-called zeroth-order approximation model, whose validity is highly dependent on the value of the perturbation parameter.