Abstarct: In this thesis, we design a new robust fault detection for linear time-invariant fractional-order systems (FOSs) assumed to be affected by sensor, actuator and process faults as well as disturbances. The observer-baxsed method was employed to solve the problem, where the detector is an observer. The problem was transformed into the mixed H_∞/H_- robust optimization problem to make the system disturbance-resistant on one hand and fault-sensitive on the other hand. Then, sufficient conditions were obtained to solve the problem in the LMI mode. Finally, the effectiveness and superiority of the method were demonstrated by simulating the solutions on a single-input multi-output thermal testing bench. In another part of this thesis we propose the analysis and design scheme of simultaneous fault detection and control (SFDC) for linear continuous-time fractional-order systems (FOSs). In essence, this simultaneous design unifies both the control and the detection modules into a single unit that is called the controller/detector unit. This unit is designed such that it generates two signals, namely the residual and the control signal. The system can be stabilized using the control signal, and the residual signals can be detected fault baxsed on model-baxsed fault detection and isolation (FDI) algorithms. The SFDC module should be designed so that the effects of faults and disturbances on the residual signals are maximized and minimized, respectively. To this end, the SFDC problem is formulated as the mixed H_-/H_∞optimization problem. Stability and fault detection are both considered through certain performance indices, and new sufficient conditions in the form of linear matrix inequalities (LMIs) are obtained. Finally, some simulation examples are given to illustrate the effectiveness of the proposed design method.