Over the past years, the automotive industry has seen a constantly increasing level of automation of automotive vehicles. This increasing level of automation contributes to an increasing safety in traffic and a reduction of traffic congestions due tio faster response times and higher reliability, with respect to the human driver. The automation of a vehicle over the longitudinal and lateral degree of freedom requires additional safety measures to ensure safety of the passengers during automated maneuvers. In a lateral control scenario, the fault detection and isolation of faults occuring in the steering system belongs to these set of safety measures. By detecting and isolating faults of interest in this system, a decision process follows which will, for example, either compensate for the acting fault or bring the vehicle to a safe standstil in the case that the fault surpasses a non-acceptable threshold. This work presents a set of novel methods for fault detection and isolation for a generalized set of linear time-invariant and parameter-varying systems. The faults under investigation comprise of an additive fault acting as an offset on the system and a multiplicative fault acting non-linearly on a set of known signals. Furthermore, the system is subjected to exogenous disturbances. The first challenge imposed is the lack of isolability of the additive and multiplicative fault using conventional linear estimation techniques. The second challenge imposed is the design of a fault detection mechanism for linear parameter-varying systems subject to exogenous faults and disturbances. The first contribution of this research is a moving least-squares based approach as an extension to an existing nullspace computation based parity-space fault detection filter. This novel combination allows a decoupled estimation of the additive and multiplicative fault. The second contribution is an extension to the first contribution by attacking one of the largest sources of error: the dynamical content of the parity-space filter. The estimation performance of the combined fault detection and isolation filter of both contributions is provided with a guaranteed performance bound, providing not only an intuitive tool to push down the estimation error, but also shows possible trajectories for future work. The third and final theoretical contribution is the adaption of the linear time-invariant parity space method for a linear parameter-varying environment. A convex quadratic optimization problem is used which has an exact analytical solution for approximately rejecting the parameter-varying effects of the system. A contribution of the more practical aspect of this thesis, is a demonstration of the applicability of the developed framework on real-life problems, both in a simulation setting and an experimental setting. The theoretical framework has been applied in a practical case study in fault detection and isolation for lateral control of autonomous vehicles. In this application, there is a particular interest in detecting and isolating the additive and multiplicative fault, acting on the steering mechanism of the vehicle, for compensation or decision making of the autonomous system in faulty scenarios. The experimental results confirm the theorems, showing that the faults can be detected and isolated both in theory and in practice.