LMI optimization approach on robustness and H∞ control analysis via disturbance-observer-based control for uncertain systems

This paper investigates the robustness of disturbance-observer-based control (DOBC) for a class of nonlinear systems with disturbances. The disturbances are supposed to include two parts. One part is the structural parameter uncertains. The other part is the unknown external disturbances supposed to be generated by an exogenous system. The unknown external disturbances also have perturbations supposed to have the bounded H₂-norm. The DOBC robust controller is combined of two parts:one is a linear feedback controller designed using LMIS and the other is a compensatory controller designed with the output of the disturbance observer. By choosing an appropriate Lyapunov function candidate, the stability of the closed-loop systems is proved.