Robust Disturbance- Rejection for a Class of Nonlinear Systems

This paper presents a robust disturbance-rejection method for a system with a time-variant nonlinearity and a disturbance. The nonlinear dynamics which satisfies Lipschitz condition is unknown. The disturbance is also unknown but bounded. Taking advantage of stable inversion, an improved EID (IEID) is utilized to deal with the total effect of the nonlinearity and disturbance. To reduce the conservativeness of system design, a feedback control gain is obtained in prior to the control gains of the observer and the IEID estimator. Then a Lyapunov functional considering the information of the nonlinearity is constructed and based on that, a linear-matrix-inequality (LMI)-based stability condition is derived to acquire the gains of the observer and the IEID estimator. Two tuning parameters are introduced in the LMI to enable the adjustment of disturbance-rejection performance. Finally, simulations for a flight control system show that the developed method has good robustness. Comparisons with disturbance-observer-based control (DOBC), composite DOBC and $H$ oo control, and conventional EID-based control methods demonstrate the effectiveness of the developed method and its advantages over others.

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