Discrete-Time Sliding Mode Control for Linear Systems with Matching Uncertainties

Sliding mode control is investigated for a discrete-time system with uncertainties. The narrowest neighborhood of the sliding surface is shown in which the state can remain. The range is determined by the upper bound of the absolute value of the uncertainty and the equation of the sliding surface. A sliding mode control algorithm is proposed to keep the state there without requiring an enormous input. Under the presence of the system parameter variations, the origin is not always stable although the sliding surface represents the stable dynamics and the state is kept in this neighborhood. The condition for the origin to be stable is investigated. Furthermore, the problems occurring when a continuous-time sliding mode control being ...