| The phenomenon of stochastic switching, such as the changes of working environment, failures of system components, system time delays, and shift of working points of nonlinear systems, can be readily found in various pratical systems. Stochastic switching systems, due to their advantageous capability of modeling these phenomena, have been extensively investigated over the past decades. As an important class of stochastic switching systems, many systematic results on Markov jump systems(MJSs) are available in the literature. However, there still exist some challenging control issues that need to be dealt with, for example, the control issues for the MJSs with asynchronous switching, and the nonlinear MJSs. Besides, the conservatism of some previous results can be further reduced. On the other hand, since semi-Markov jump systems(S-MJSs) relax the Markov property or the non-aftereffect property(Markov property) of transition probabilities(TPs), they generalize the scope of stochastic switching systems and thus become a naturally extended research frontier. However, the generality of S-MJSs, i.e., the property that the TPs can depend on the historical knowledge of mode switching sequence, unavoidably leads to the considerable complexity in studying the S-MJSs, even for the basic stability issues.This paper focuses on the stability analysis and state estimation problem for a class of complex stochastic switching neural networks, and based on the above sorts of consideration, this paper will research a special kind of stochastic switching system. The particularity is mainly embodied in the specificity of switching signal, which examines the stochastic switching system between each mode switching by semi-Markov chain. This not only covers the traditional research work based on the Markov chain(Markov chain can be regarded as a special kind of semi-Markov chain), and makes the conclusion more practical significance. At the begining, this paper introduces the mathematical tool of semi-Markov Kernel to derive the control theory; At the same time, the probability density function of dwell time will depend on both the current and next system mode, which makes the distribution of different types and different distribution parameter of the probability density function of dwell time can exist at the same time to depict the different mode transition probability characteristics from the same mode to a different mode, which makes the study of this paper more general; In addition, this paper also puts forward a new concept of stability, not only expands the definition of traditional mean square stability, but also enables the stability criterion contain all the information in probability density function of dwell time, and practical application value can also be measured.Based on the above research, the structure of this paper is roughly arranged as shown below:Chapter 1 illustrates the motivations on the research of the task, presents the domestic and foreign literature review of S-MJSs, and introduces the main research content.Chapter 2 bases on the references, will study the semi-Markov Kernel, the mean square stability and some classical matrix transformation, give necessary mathematical definition and preliminary proved theory to make described in subsequent chapters content more compact.Chapter 3 researches the problem of stability analysis and state estimation for a class of traditional Markov jump linear system, which lays a foundation for the semi-Markov jump linear system.Chapter 4 aims at a class of stochastic switching system(the switching signal has the particularity), i.e., the semi-Markov jump linear system, and establish the stability criterion.Chapter 5 utilizes a class of time-varying Lyapunov function method, study the state estimation problem of semi-Markov jump neural network systems and design a H? filter.Respectively, numerical examples are presented to illustrate the validity and advantage of the developed theoretical results at the end of Chapter 3, Chapter 4, Chapter 5. |
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