Circumventing the Relative Degree Condition in Sliding Mode Design

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A continuous time sliding mode is generated by means of discontinuities in the applied injection signals, about a surface in the state space [17, 33, 40]. The discontinuity surface (usually known as the sliding surface) is attained from any initial condition ideally in a finite time interval. Provided the injection signals are designed appropriately, the motion when constrained to the surface (the sliding mode) is completely insensitive to so-called matched uncertainties, i.e. uncertainties that lie within the range space of the matrix distributing the injection signals. Much early work in this area related to control problems and assumed all of the states were available for use both in the switching function evaluation and also by the control law. For practical application however, the case when only limited state information is available is of interest.