In this paper, an observer-based \(H_\infty \) control problem is studied for a class of switched cyber-physical systems over amplify-and-forward relay networks with double fading channels. An AF relay is deployed between sensor and controller with hope to enhance the communication range. In this relay-based network, the relay first receives the data from the sensor and then transfers it to the controller. Further, double fading channels are considered in both the sensor to relay channel and the relay to controller channel, whose coefficients are described by two series of random variables. The application of Lyapunov stability combing with average dwell time technique first leads to the derivation of a sufficient condition for guaranteeing the stability and \(H_\infty \) performance of the controlled system. Subsequently, the desired gains of the observer-based controller are parameterized by solving a set of matrix inequalities. Finally, two examples are offered to showcase the applicability of the presented control strategy.
