It is well-known that sliding mode control is robust to matched uncertainties that lie in the range space of the input matrix. However many systems are affected by mismatched uncertainties and yet do not enjoy the matching conditions. It is the purpose of this paper to present a new dynamical approach of sliding variable formulation which, when the system is in sliding mode, can explicidy deal with mismatched uncertainties. Our first step is to treat certain states as inputs to a reduced-order system and use adaptive techniques to design fictitious controllers for these inputs, which can then tackle the mismatched uncertainties. The second step is to use sliding control to realize the adaptive fictitious controllers. The design is systematic, modular and intuitively simple. 1. Introducdon Consider the regulation of the following controllable single-input system: *I = (All + ~~I)XI + (Arz + u,z)xz (la) xz = (A*, + AA2,)x, + (AZ2 + A&,)x, + (b + Ab)u, b > 0, (lb) where u, xz, AZ2 are in R' x,, A,,, A$ are in R"-' A,, is in R(n-')x(n-').
A(.) denotes uncertainties in (.). Tracking and MIMO systems can be similarly treated.
Usually the sliding variable is defined as (for example,