Fault-tolerant Control Of Uncertain Time-delay Descriptor Bilinear Systems

In recent years, the fault-tolerant control problem of descriptor systems is paid more and more attention in the field, and most results are for linear systems.Related results for nonlinear systems are fewer. Therefore, the fault-tolerant control of the bilinear systems similar to the linear systems has become a hot spot, and it can more accurately describe of industrial objects in the larger range, and it has more value of research. However, in real systems, as components of aging and the delayed signal transmission, the systems will inevitably produce delays. And due to model errors, the linear approximation and the impact of environmental change, there inevitably exist uncertainties, such as Liquid delivery systems, Rolling systems. So according to two phenomena in the systems, this thesis discusses the H∞fault-tolerant control of the uncertain time-delay descriptor bilinear systems.1. When we study the fault-tolerant control problem of descriptor linear time-delay systems and the descriptor bilinear time-delay systems, we can introduce a state feedback control law with time-delay. Based on Lyapunov stability theory, for the descriptor uncertain linear time-delay systems, it proves that because of the introduction of a state feedback control law with time-delay, the closed-loop systems still possess the integrity and robustness when the sensor and actuator fail. So based on this, it presents the method of fault-tolerant control of descriptor bilinear systems with time-delay. When an actuator failure appears, the system can maintain stability and satisfy the performance index γ by the feedback controller. In the design process, it chooses the weight matrix Q properly in the Riccati equation to process the bilinear terms, and we can get matrix P. Finally, a simulated example verifies that the conclusion is valid. 2. Based on the front part of the thesis, the latter part of the thesis studies the fault-tolerant control, when the uncertain time-delay descriptor bilinear systems appear the case of actuator failures. In this thesis, the characteristic is the complexity of the systems, as a nonlinear systems, the systems are similar to the linear systems. Not only does the systems have the value in research, but also for practical application is also important. In the built systems model, it has the coefficients with uncertainties, especially in the bilinear term of the coefficient matrix. For the bilinear term in the deal, the thesis has also been innovation, and to do with the uncertain parameters matrices separately from the constant coefficient matrices. In this thesis, the parameter uncertainty, are not based on norm-bounded uncertainties in the form of this particular approach, instead of using a more general approach.3. Base on the fault-tolerant control of the uncertain descriptor bilinear systems with time-delay, this thesis also studies the H∞fault-tolerant control of the systems when the initial state is non-zero. In the derivation, we ingenious apply this condition of the initial value of the Lyapunov function4. Base on the research process, it focuses on Riccati Equation and selecting the appropriate Q by step one, solves P, and then it ensures when the actuator failures, the systems can still maintain the integrity of the sufficient condition, and we obtain the corresponding control law.