Analysis And Control For Singular Bilinear Markovian Jump Systems

Singular bilinear system, different from a linear singular system, is a kind of nonlinear singular system. Control theories and applications of nonlinear systems have always been a hot research focus due to their potentials. Meanwhile, because of their capability of system modeling linear Markovian jump systems have also been extensively studied. The focus of this dissertation is stability analysis and controller and filter design of continuous singular bilinear Markovian jump systems (SBMJSs). Futhermore, fault detection and robust fault-tolerant control are discussed. The main contributions for this dissertation are as follows:The model of SBMJSs is established and the stochastically stabilizable of SBMJSs is defined. According to this definition, state feedback controllers and output feedback controller are designed. Their existence conditions, described as LMIs, are given. Further, the design methods are extended into time-delay SBMJSs with parameter uncertainty.Robust fault-tolerant control for SBMJSs is investigated and the proper controllers are designed. The controllers, whether the actuators are normal or abnormal, could be used to stabilize the closed-loop systems stochastically, and satify required L 2norm performance index.State observers of SBMJSs are designed and applied to fault detection. Then the sufficient conditions of fault detection filter based on the observers are presented. According to this, the robust filtering problems of time-delay SBMJSs and time-delay SBMJSs with parameter uncertainty are discussed respectively.The model of SBMJSs with Wiener process is established and a stable condition is given. Then observer of SBMJSs with Wiener process is designed to estimate state vector.Finally, the corresponding numerical simulation illustrates the applicability and effectiveness of the techniques proposed above.