The safe and effective control of nuclear reactors is of significant interest to the research reactor community and nuclear power utility industry. Numerous advanced control algorithms have demonstrated superior reactor control over the past several decades - primarily on simulated reactors. Among these, state feedback control has been applied to virtually every type of dynamic system. This paper focuses on developing an accurate model of the Penn State TRIGA Reactor simulation and creating a state feedback controller/state observer design using self-powered Vanadium and Rhodium neutron detectors (SPND) as feedback sensors. This work is the first attempt to use these type of sensors in a closed-loop feedback system for reactor control. The foundation of the equations in Simulink has been derived from normalized point kinetics equations and core averaged thermal-hydraulic equations. The self-powered detector dynamics may be developed from basic activation/decay balance differential equations. Results demonstrate that the TRIGA Simulink model developed compares well with the actual TRIGA Reactor data. Self-powered neutron detectors are well-suited to monitor steady-state reactor power. Due to their dependence on radioactive decay after irradiation to produce a current signal, self-powered detectors have significant delay times associated with them, making them inadequate for real-time feedback control. The long delay associated with the normal detector models can only realistically be used for applications where this delay can be tolerated, such as post-accident power monitoring. A major contribution of this paper is the development and application of detector inverse models, which null-out delays introduced by the physics of the detector. Results demonstrate that the inverse detector models have no delay which is desirable for the reactor closed-loop control. SPNDs need no external power to produce current levels consistent with ion chambers and may prove to be a vital component for closed-loop nuclear reactor control in the future. The successful application of an advanced control algorithm i.e., state-feedback control with self-powered neutron detectors, demonstrates that this technology may be applied in closed-loop nuclear reactor control and safety systems not only for power plant applications but for applications such as space nuclear reactors as well.