A descriptor regular form‐based approach to observer‐based integral sliding mode controller design

Abstract

AbstractThis article establishes a descriptor regular form and shows its applications in observer‐based integral sliding mode controllers design of descriptor systems. A reduced‐order linear observer and a full‐order descriptor sliding mode observer are, respectively, designed to estimate the state variables of the descriptor system under consideration. Necessary and sufficient conditions for the existence of the proposed descriptor regular form and observers are derived. With the descriptor regular form, it is revealed that the separation principle holds for the proposed observer‐based integral sliding mode control methods. This means that the proposed observers can be designed independently and when using the estimation of state variables obtained from them to replace the state variables in a stabilizing state‐feedback integral sliding mode controller, the resulting observer‐based integral sliding mode controller can still stabilize the descriptor system. Finally, a constrained mechanical system is numerically simulated to verify the methods proposed.