H_∞ Control And Filtering For Markovian Jump Systems Subject To Saturation Nonlinearity And Incomplete Knowledge Of Transition Probability

Due to inherent physical limitations of the device, actuator saturation and sensor saturation arise in nearly all practical control systems. They can severely degrade the closed-loop system performance and sometimes even make an otherwise stable system unstable.On the other hand, Markov jump systems, as a special class of stochastic hybrid systems, has been an attractive subject of research during the last decades. This class of systems has found a wide range of applications in various fields such as manufacturing systems, networked control systems etc.So far, many analysis and synthesis results have been reported under assumption that complete transition probabilities are known. In practice, however, the likelihood of obtaining ideal knowledge on all transition probabilities is actually questionable, since the cost is probably high or large complexity to measure. Therefore, it is significant and necessary to further study more general jump systems with incomplete knowledge of transition probability. This thesis is organized as follows:Firstly, the H∞control problem of continuous-time Markov jump systems subject to saturating actuator and incomplete knowledge of transition probability is addressed. By introducing some free-connection weighing matrices, a much larger estimate of domain of attraction in mean square sense and an H∞performance index can be obtained.Secondly, we consider the H∞control problem of discrete-time Markov jump systems. By designing an H∞mode-dependent controller that will stochastically stabilize the closed-loop system, we provide an H∞performance index and domain of attraction in mean square sense.Finally, the set-membership filtering problem of Markov jump systems subject to sensor saturation and incomplete knowledge of transition probability is considered. By providing a set of ellipsoidal state estimates which always contains the true state of the system, the state of system can be well tracked.