Sliding Mode Control with State Derivative Output Feedback in Reciprocal State Space Form

This paper investigates the novel sliding mode control design with state derivative output feedback in nontraditional reciprocal state space (RSS) form. The concepts and the need of RSS form are comprehensively reviewed and explained. Novel switching function and approaching condition based on the derivative of sliding surface are introduced. In addition, a sufficient condition for finding the upper bound of system uncertainty to guarantee the stability in sliding surface is developed for robustness analysis. A compact sliding mode controller utilizing only state derivative related output feedback is proposed for systems with system uncertainty, matched input uncertainty, and matched external disturbance. Simulation results for a circuit system successfully verify the validities of the proposed algorithms. Our derivation is basically parallel to that for systems in standard state space form. Therefore, those who understand the concepts of sliding mode control can easily apply our method to handle more control problems without being involved in complex mathematics.