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This article consists of two parts: a theoretical part concerned with fault detection schemes, and an application part dealing with cyber security of power systems. In the first part, we develop a tractable approach to design a robust residual generator to detect and isolate faults in high dimensional nonlinear systems. Previous approaches on fault detection and isolation problems are either confined to linear systems or they are only applicable to low dimensional dynamics with more specific structures. In contrast, we propose a novel methodology to robustify a linear residual generator for a nonlinear system in the presence of certain disturbance signatures. To this end, we formulate the problem into the framework of quadratic programming which enables us to solve relatively high dimensional systems. In the second part, the application is motivated by the emerging problem of cyber security in power networks. We provide description of a multi-machine power system that represents a two-area power system, and we model a cyber-physical attack emanating from the vulnerabilities introduced by the interaction between IT infrastructure and power system. The algorithm developed in the first part is finally used to diagnose such an intrusion before the functionality of the power system is disrupted.