| Stochastic Markov jump systems, which describe many engineering and social problems, need to be investigated for its theoretical and engineering value. As a class of hybrid systems, its states are constituted by two parts: the discrete part describes the mode of the system, and the continuous part describes the dynamic process of the system.As the development of science and technology, the industrial facilities are getting more and more complicated, and the safety and reliability of the system have attracted much attention of scholars. Especially for those big facilities like aircrafts and space shuttles, any malfunction of a tiny part that has not been conducted properly may result in huge loss of money and even the casualties. In the era of highly-developed control technology, we should consider the malfunction and reactivating of the system when we design it. The safety and reliability have become two major objectives when designing and developing control systems. Under such background, fault-tolerant control method that was firstly developed in the 1980s is such kind of control technology which aims to enhance the reliability of the systems. It means taking effective measures when failures happen so as to make sure the system still runs safely, effectively and reliably. Sometimes, we need to trade off some performance so as to secure the reliability of the system.This thesis investigates the Markov stochastic jump systems and descriptor jump systems with norm-bounded parameter uncertainties. Based on the Lyapunov stability theory for stochastic jump systems, we have investigated the design methods of controllers with completeness when the actuator fails to work. Through solving a couple of LMIs, we arrive at the controller that stabilizes the system when the actuator fails. Furthermore, we require the closed-loop system to satisfy the H∞performance when suppressing the noises.We have testified the feasibility of our methods in the end of every chapter with an example and simulation. |
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