Abstract:

By combining the sliding mode control for mismatched uncertainties with the linear matrix inequality（LMI）approach，a novel robust sliding mode observer for a class of uncertain dynamic system with mismatched uncertainties was designed. The necessary and sufficient condition of stabilizing the sliding mode observer and the LMI existence theorem were presented and strict verification was done to guarantee robustness to uncertainties of systems and disturbances. The Lyapunov function was used as the judgement condition for stabilizing observers，and the convergence rate between observer and system was changed by regulating the sliding-mode strategy so as to attain the desired performance of state estimation. Simultaneously，without the canonical transformation of the dynamic systems，the linear feedback matrix and nonlinear feedback matrix of the robust sliding mode observer were solved by LMI that has advantages in computation. The problems of actuator fault detection and reconstruction for a class of uncertain dynamic system with mismatched uncertainties were discussed. By applying the equivalence output error concept and LMI approach，the optimizing strategy of reconstructing actuator fault can be designed，and a new actuator fault detection and reconstruction design method based on the designed sliding mode observer was proposed to obtain the fault information on-line. The design procedure was described and nonlinear simulation results were presented to demonstrate the approach.