Research On Robust Fault Detection For Markovian Jump Systems

Markovian jump systems are demonstrated to be very appropriate to model plants whose structures are subject to random abrupt changes, due to, for instance, sudden environment changes, transition of subsystem interconnections, change of the operating point of a linearised model of a nonlinear systems, and so on. This kind of systems can be used to represent many important physical systems, such as manufacturing systems, electric power systems, communications systems, aircraft flight systems etc. In order to ensure the system safety and reliability, researches on robust fault detection for Markovian jump systems are not only theoretically interesting, but also very significant in practical applications. The purpose of this dissertation is to investigate fault detection for Markovian jump systems with L2-norm bounded unknown input, polytopic uncertainties, time-delays, and singular Markovian jump systems with L2-norm bounded unknown input. The main results of this dissertation are as follows.1. For a class of continuous-time Markovian systems with L2 norm bounded unknown input, an adaptive observer-based robust fault detection approach is proposed. By using a mode-dependent adaptive Markovian jump observer as residual generator, the robust fault detection filter design problem is formulated in the framework of stochastic H∞filtering problem. By applying linear matrix inequality technique, sufficient conditions on the existence of robust fault detection filter are derived, and the solutions are also given.2. For a class of continuous-time Markovian jump systems with both unknown inputs and Polytopic uncertainties, the stochastic H∞filtering formulation of fault detection is proposed. Both mode on-line available and on-line unavailable cases are considered, and by applying parameter-dependent stochastic Lyapunov function and introducing slack matrices, the solvable conditions of this problem are derived in terms of linear matrix inequalities.3. The problem of adaptive observer-based robust fault detection for time-delay Markovian jump systems. An adaptive Markovian jump observer with state delay is constructed as residual generator. Applying stochastic Lyapunov-Krasovskii functional approach and introducing slack matrices, delay-dependent sufficient conditions are derived to ensure that the robust fault detection filter design problem is solvable, and the solutions to the parameter matrices are also given.4. The problem of H∞filtering based robust fault detection for continuous-time singular Markovian jump systems is investigated. Both mode on-line available and on-line unavailable cases are considered, and sufficient conditions on the existence of the robust fault detection filter and parameter matrices to the fault detection filter are derived in terms of linear matrix inequalities.5. The problem of parity space-based fault detection and fault estimation problem for a class of discrete-time Markovian jump systems is studied. For fault detection problem, the unified solution to the parity matrices is given by using singular value decomposition, and a new recursive algorithm is developed to reduce the numerical computation. For fault estimation, some design criteria is introduced to evaluate the fault estimation performance index, and a relationship between the parity space-based fault estimation and the minimum problem of certain matrix quadratic form is built. Based on this, a necessary and sufficient condition for the minimum problem is derived, and a unified analytic solution to the parity matrices is obtained.