Robust sampled-data control of structures subject to parameter uncertainties and actuator saturation

This paper presents a robust sampled-data controller design approach for vibration attenuation of civil structures considering parameter uncertainties and actuator saturation. The parameter uncertainties belong to polytopic form and are assumed to be the variations of the structural stiffness and damping. Regarding the uncertain sampling problem encountered in real world applications, the sampling period designed for the controller is allowed to be variable within a given bound. In order to obtain reduced peak response quantities, the energy-to-peak performance used to describe the peak values of the control output under all possible energy-bounded disturbances is optimised. The robust sampled-data state feedback controller is obtained in terms of the solvability of certain linear matrix inequalities (LMIs). The applicability of the proposed approach is demonstrated by a numerical example on vibration control of a building structure subject to seismic excitation. It is validated by the simulation results confirming that the designed controllers can effectively attenuate the structural vibration and keep the system stability while there are parameter uncertainties and actuator saturation constraints.