Analysis And Syntheses Of Several Kinds Of Markovian Jump Systems With Generally Uncerntain Transition Rates

This paper focuses on the investigation of the stability and stabilization problem of the three types of Markovian jumping systems. It consists of four chapters:Chapter I is the introduction part, which focuses on the source of the subject, the background and significance of the research.In the second chapter, we explore the stabilizability of delayed singular Markovian jumping system with uncertain transition rates. Based on the method of linear inequalities, we design a state feedback controller and present some criteria on stability of the error system and dynamic equation which satisfy a certain level of disturbance attenuation index. At the end, examples are provided to illustrate the effectiveness of our results.In chapter III, we investigate the stability problem of Markovian jumping singular systems with generally uncertain rates and Brownian process. In the system, the transition probability is uncertain. The range of the transition probability is known, or the transition probability is completely unknown. First of all, we describe the target model and give some preparations. Secondly, the controller is designed for the singular Markovian jump system subject to general uncertainty transition rate, to ensure the stochastically stability within the given disturbance attenuation index. At the end,examples are provided to illustrate the effectiveness of our results.In chapter IV, we study a class of global exponential stability of delayed Markovian jumping fuzzy cellular neural network system with general uncertain transition rates. In the system, the transition probability is uncertain. The range of the transition probability is known, or the transition probability is completely unknown.Based on linear matrix inequality technique and Lyapunov theory, some global exponential stability criteria are given in the form of LMIs. Examples are provided to illustrate the effectiveness of our results.