随着工业系统复杂性的快速提高，故障对系统的影响也越来越不可避免。因此，及时地发现故障并对其进行有效地处理，是保证系统安全运行的前提条件。由于工业中存在大量有迫切的实际需求，故障诊断已成为当前学术界和工业界广泛关注的领域。 任何实际系统都在一定程度上受到扰动、噪声等不确定性因素的影响。论文对这些不确定性因素采用集合的形式进行处理，考虑了系统可能出现的最坏的情况，研究了基于集理论的鲁棒故障诊断算法，并分别在固定翼和四旋翼无人机模型上完成了仿真验证。本论文的主要工作如下： 1）阐述了不变集和区间观测器两种集理论方法完成故障检测的基本原理，从残差信号集、计算复杂度和故障检测保守性三个方面比较两种方法的优缺点。 2）联合不变集和区间观测器两种方法，将区间观测器的应用从故障检测推广到故障隔离。利用不变集理论预先给出了故障可检测与隔离的条件，只要满足条件的任何故障均能被检测与隔离出来，同时完成了传感器和执行器区间浮动故障检测与隔离算法设计。 3）将集理论方法与未知输入观测器结合起来，提出集理论未知输入观测器概念，并基于集理论未知输入观测器设计主被动联合鲁棒故障诊断算法，有效地解决了未知输入观测器完成故障诊断的存在性问题，降低了单纯集理论方法故障诊断的保守性，提高了故障诊断灵敏度。 4）将提出的执行器区间浮动故障诊断算法应用在固定翼无人机上，完成固定翼无人机纵向运动中推力杆和升降舵故障诊断仿真验证。将提出的主被动联合鲁棒故障诊断算法应用在四旋翼无人机上，完成四旋翼无人机悬停状态下的螺旋桨故障诊断仿真验证。 基于集理论的鲁棒故障诊断算法的优势在于它能提供鲁棒的故障检测与隔离决策。一旦算法检测出故障，那么系统故障必定真实发生，不存在虚警率的问题。实际系统不可避免会受到不确定性因素的影响，一般来说，这些不确定性因素的能量都是有界的，方便用集合形式建模处理。因此，论文研究的基于集理论的鲁棒故障诊断算法具有一定的工程实用性。

With the increasing complicity of the industrial systems, it is inevitable for them to be influenced by faults. In order to guarantee the safe operation of systems, it is important to detect and handle the faults in time and effectively. Considering a large number of urgent needs, fault diagnosis has been raising wide attention in the academic and industrial communities. It is known that any real system is always influenced to some extent by some uncertainties including process disturbance, measurement noise and so on. In this dissertation, taking the worst case of a system into account, we proposed to utilize the set theory to model and deal with these uncertainties and put forward set-theoretic robust fault diagnosis algorithms, which has been successfully applied to the fixed-wing and quadrotor UAV (unmanned aerial vehicle). The main contents of this dissertation are as follows:1) The FD (fault detection) principles of invariant sets and interval observers are briefly illustrated. The two FD approaches are compared with each other from three aspects including residual sets, computational complexity and FD conservatism, and their advantages and disadvantages are further analyzed. 2) Combining invariant sets with interval observers, we extend interval observers from the FD to FI (fault isolation) applications. Especially for FI, invariant sets are used to construct fault signature matrix off-line, which gives guaranteed FDI (fault detection and isolation) conditions. Any type of faults satisfying the guaranteed FDI conditions can be detected and isolated. Meanwhile, the detection and isolation algorithms of unknown but bounded faults in actuators and sensors were proposed.3) The notion of SUIO (set-theoretic unknown input observers) was put forward by combing passive set-theoretic FD and active UIO (unknown input observers) FD. Mixed active/passive robust FDI algorithm with SUIO was proposed to effectively solve the existence problem of UIO in FD and improve the sensitivity of fault diagnosis by reducing the set-theoretic FDI conservatism.4) The proposed detection and isolation algorithm of unknown but bounded actuator faults was applied to the FDI of thrust lever and elevator of the fixed-wing UAV in the longitudinal motion. Moreover, the proposed SUIO-based mixed active/passive robust FDI algorithm was applied to the quadrotor UAV at hovering.The main advantage of set-theoretic robust FDI algorithm consists in that it can provide robust FDI decisions. Once faults are detected by the proposed algorithm, the faults must have occurred in the real system, which means that there exists no false alarm rate problem for the set-theoretic approaches. Since real systems are always under the influence of some uncertainties and in general, the energies of these uncertainties are limited, which can be conveniently modeled and handled using the set theory. Therefore, this implies wide applications of the proposed set-theoretic robust FDI algorithms in engineering systems.