I. Introduction
Sliding-mode control (SMC) [1] is a well-known robust control design approach. The fundamental idea of sliding-mode control is to constrain the system trajectory on a predesigned hyperplane by a switching input. The greatest advantage of sliding-mode control is its inherent insensitivity to uncertainties and disturbances which satisfy a certain structural condition called a matching condition. A standard sliding-mode controller is designed in two steps. First, a sliding surface on which the system dynamics is governed is selected. Second, a switching control law to enforce the system trajectory on the selected surface is determined. A large number of SMC design methods [2]–[5] for finite dimensional systems and a mathematical extension of differential inclusions to aftereffect systems [6] have been proposed, and several approaches have been developed for the SMC of linear time-delay systems [7]–[16]. However, few approaches have been proposed for nonlinear systems with time-delay. A solution based on polytopic models was proposed in [17]. Bonnet et al. [18] considered linear, time-invariant and bounded-input–bounded-output (BIBO) stable plants possessing a delay in the numerator. The output is measured via a relay sensor, and the result can be extended to saturated sensors. The result involves a “local inverse” of the sign operator. This means that this “inverse” has to be computed for a predefined reference signal, e.g., a sine function. The approach proposed herein is different from these methods.