Robust H-infinity state feedback control for switched linear systems with linear fractional uncertainties based on LMI

In this paper, we address robust H-infinity state-feedback control for switched linear systems with linear fractional time-varying uncertainties using LMI (linear matrix inequality) approach. First, for a class of unforced switched linear systems, a sufficient condition is derived for asymptotic stabilization with a prescribed disturbance attenuation level only by employing a state-depended switching strategy based on LMI method. Then the robust H-infinity control synthesis via switched state feedback is studied for switched linear system with linear fractional time-varying uncertainties. It is shown that a switched state-feedback controller can be designed to stabilize asymptotically the uncertain switched linear systems with an H-infinity norm bound if a linear matrix inequality condition is feasible under the associated parameters are selected in advance. All the results presented in this paper can be regarded as an extension of some existing results for switched and non-switched linear systems.