Robust Switched State Feedback design for linear uncertain systems subject to disturbances

A state feedback design for linear uncertain sys-tems is proposed. To attenuate the effect of disturbances on the output of the system two performance indexes are included in the control design. For $\mathcal{L}_{2}$ disturbances the results ensures that the closed loop system has an $\mathcal{H}_{\infty}$ guaranteed cost and for $\mathcal{L}_{\infty}$ disturbances a L
1
performance index is achieved. The stabilization conditions are given in terms of LMIs. To improve the control performance and relax the LMI conditions a switched controller which avoids chattering is proposed. Numerical examples illustrate the efficiency of the stabilizing conditions.