Further results on variable output feedback controllers

Zak and Hui [1] proposed a sliding mode controller for linear multiple-input-multiple-output (MIMO) systems using static output feedback. The note in [2] provided an improvement of the output feedback controller in [1] for a class of linear single-input-single-output (SISO) systems that eliminated two important limitations of [1]: (a) system uncertainties must be bounded by the system output; and (b) a requirement of a matrix inequality [1, eq. (4-3)]. The controller in [2] can guarantee global closed-loop stability. This note extends the results of [2] to linear MIMO systems. It is emphasized that the proposed MIMO controller yields global closed-loop stability whereas the one in [1] can only guarantee local stability. An application of the proposed MIMO controller to an aircraft model is included to show the effectiveness of the method.