A robust nonfragile observer-based controller for a linear time-invariant system with structured uncertainty is introduced. The [ ] robust stability of the closed-loop system is guaranteed by use of the Lyapunov theorem in the presence of undesirable disturbance. For the sake of addressing the fragility problem, independent sets of time-dependent gain-uncertainties are assumed to be existing for the controller and the observer elements. In order to satisfy the arbitrary H₂-normed constraints for the control system and to enable automatic determination of the optimal [ ] bound of the performance functions in disturbance rejection control, additional necessary and sufficient conditions are presented in a linear matrix equality/inequality framework. The [ ] observer-based controller is then transformed into an optimization problem of coupled set of linear matrix equalities/inequality that can be solved iteratively by use of numerical software such as Scilab. Finally, concerning the evaluation of the performance of the controller, the control system is implemented in real time on a mechanical system, aiming at vibration suppression. The plant under study is a multi-input single-output clamped-free piezo-laminated smart beam. The nominal mathematical reduced-order model of the beam with piezo-actuators is used to design the proposed controller and then the control system is implemented experimentally on the full-order real-time system. The results show that the closed-loop system has a robust performance in rejecting the disturbance in the presence of the structured uncertainty and in the presence of the unmodeled dynamics.

This paper presents a disturbance rejection-based solution to the problem of robust output regulation. The mismatch between the underlying plant and its nominal mathematical model is formulated by two disturbance classes. The first class is assumed to be generated by an autonomous linear system while for the second class no specific dynamical structure is considered. Accordingly, the robustness of the closed-loop system against the first disturbance class is achieved by following the internal model principle. On the other hand, in the framework of disturbance rejection control, an extended state observer (ESO) is designed to approximate and compensate for the second class, i.e., unstructured disturbances. As a result, the proposed output regulation method can deal with a vast range of uncertainties. Finally, the stability of the closed-loop system based on the proposed compound controller is carried out via Lyapunov and center manifold analyses, and some results on the robust output regulation are drawn. A representative simulation example is also presented to show the effectiveness of the control method.