The use of sampled-data systems is abundant in industry due to many developments in digital technology. In sampled-data systems, the process under control is continuous-time but the controller is implemented in discrete-time. In many practical and industrial applications, sampled-data systems operate non-uniformly. In these systems, the output sampling and control signal updating occur in the unequally distributed time instants. Communication network limitations, human factors, unpredictable delays in sensors and measurement devices as well as delays in providing data in chemical and industrial processes are some of the reasons that make systems operate non-uniformly. One of the most important issues about sampled-data systems is controller design. There are some difficulties in controller design for non-uniform systems. In these systems, when the data is delivered to the controller as well as the time the control signals are updated are not predictable. Therefore, the controller does not know when the data will be provided. Thus, these systems are inherently time-varying and the controllers should also be time-varying. Implementing such controller is difficult. On the other hand, methods used to design controllers cannot be explicitly utilized for non-uniform systems. Since these systems are time-varying, concepts such as Z-transform and H 2 -norm do not apply and controller design cannot be done in frequency domain. Therefore, controller design must be done in time domain. Because of the difficulties mentioned, controller design problem for non-uniform sampled-data systems has not been resolved completely. In this thesis, H 2 controller is designed for non-uniform sampled-data systems. In uniform sampled-data systems, this controller minimizes the 2-norm of the system impulse response. Non-uniform systems are time-varying and H 2 -norm has not been defined for time-varying systems. So first the H 2 -norm definition is extended for non-uniform sampled-data systems and then the controller is designed for these systems. The controller is designed using three methods: first indirect method, second indirect method and direct method. Finally, through a case study, the H 2 controller is designed for a linearized ball and beam system with all methods and the results are compared. Key Words: Sampled-data Systems, Non-uniform sampling, H 2 Controller, Linear Matrix Inequalities