On variable structure output feedback controllers

In a recent work by Zak and Hui [1], a sliding-mode controller for multi-input/multi-output (MIMO) systems using static output feedback was proposed, Very nice geometric conditions for how to design sliding surfaces were given, However, there are two restrictive assumptions in it, One is that the uncertainties in the system must be bounded by a known function of outputs which excludes some possible uncertainties in the A matrix if the system is described by the triple (A, B, C). The other one requires a matrix equality [1, (4.3)] to be held which may also be very difficult to satisfy in many systems. In this paper, we propose a modification of the sliding mode controller for a class of single-input/single-output (SISO) systems which can eliminate the above-mentioned limitations and, under certain conditions, guarantee global closed-loop stability, Hence the range of applicability of the method in [1] can be greatly broadened.