Equivalent-Input-Disturbance-Estimator-based Control Design for Polynomial Fuzzy Systems

This paper deals with the disturbance rejection problem for polynomial fuzzy system based on the estimation of an equivalent-input-disturbance (EID) approach. The EID estimator approach is used to compensate the influences of unknown bounded exogenous disturbance and uncertainties on the output of the system. Precisely, EID-estimator approach contains polynomial state observer and low-pass filter, which helps to estimate unknown system states and influence of the unknown disturbance signals. To cope the stability and lumped disturbance estimation problems simultaneously, the augmented closed-loop system is constructed that includes dynamics of the system, observer, and low-pass filter. The required stability conditions of resulting augmented system are developed with the aid of Lyapunov stability theory. Furthermore, they are expressed in the form of sum-of-square (SOS) constraints that can be solved via Matlab SOSTOOLS. Finally, a numerical example is provided to demonstrate the viability of the design approach for synthesizing a stabilizing controller and disturbance rejections.