Formula omitted] fuzzy observer-based dynamic sliding mode control: Unknown input rejection approach

Abstract

This article presents an H∞ fuzzy dynamic observer-based dynamic sliding mode control (SMC) for continuous-time Takagi-Sugeno (T-S) fuzzy systems in the presence of external disturbances and uncertainties. Compared with the conventional SMC and the existing approaches, the effects of the unknown input signals whether linear or nonlinear are completely eliminated. Furthermore, the nonlinear systems which are modeled as T-S fuzzy systems are allowed to share different input matrices under the proposed SMC. The matrix gains of the proposed dynamic sliding surface are derived from the solution of the linear matrix inequalities (LMIs). In addition, an H∞ fuzzy dynamic observer is proposed based on a new approach for T-S fuzzy systems affected by uncertainties and external disturbances. To reduce the analytical complexity and avoid the non-convex problem, a new transformation is used to propose both dynamic sliding surface and the dynamic observer. The stability conditions are extracted also in form of an optimization problem. Lastly, a Translational Oscillator with an eccentric Rotational proof mass Actuator (TORA) system is simulated with the proposed methods to show the superiority and effectiveness.