Sliding Mode Control Theory & Applications

The system theory with variable structure has been the object of multiple studies for about fifty years. The first work on this kind of systems is those of Anosov, Tzypkin and Emelyanov in the former USSR, or those of Hamel in France. This research made new great strides at the end of the Seventies when Utkin introduces the theory of the sliding mode. Currently, this technique knows a broad range of applications in very varied fields such as robotics, mechanics and the electro-technology. The algorithm by sliding mode control is classified in the monitoring systems with variable structure VSS (Variable System Structure in the Anglo-Saxon literature). This technique is based on the principle of reduction of the systems’ order and it concern linear and nonlinear systems. The principle of system with variable structure consists in bringing back, whatever the initial conditions, the point representative of the system evolution on a space surface (representing a set of relations, static, between the variables of state).