The Design Of State Obserber Of The Complex Dynamical Networks With Sampled Data

With the development of digital technology, information technology and networks, it is unavoidable for human beings to live in the situation that our lives involve all kinds of digital equipment. In this case, we have to sample the data to transmit or get the information of the digital equipment. Moreover, as we only can interconnect with the digital instruments by sampling information, we have to study further of this field of data-sampling, which has a significant and farreaching impact on people.At the same time, as we all know that the complex dynamical networks(CDN) reflect some specific characters of the nature, it is crucial to study further of the CDN, which has arouse the extensive attention of the experts and researchers from domestic and overseas. One of the central issues of the theory of CDN is about the design of sate observer, so in this paper, it focus on studying the design of the state estimation of the CDN with multi-rate sampling based on the stability theory of Lyapunov.The main study points are displayed as follows:Firstly, we study the state estimation of state coupled CDN with multi-rate samplers, that are based on the approach of in-put delay, and the sampling period switch between r different values in a random way with given probability. When transmitting the data among nodes, some uncertain noise are considered. We use the error between the real states of nodes and the observed data of nodes and the deviation between estimated output data and the real output data as the feedback control signal of integral controller, while using the deviation between observed output data and the real output data as the ratio control signal. Then the theory of new adaptive controller of this state observer is given, which is based on the stability theory of Lyapunov-Krasovskii and LMIs. In the end, several numerical examples are given to demonstrate the effectiveness and the excellence of the new adaptive controller.Secondly, considering the output coupled CDN, we get the output of the nodes and design the state observer by separate samplers. And we use the sampled output value of state observer as the feedback of estimation controller. Simultaneously, we use method of the input delay as sampling period, where the data have two different time-varying delay randomly happen between two intervals which have different lower and upper bounds are known. Then we derive the theory of state observer from the stability theory of Lyapunov-krasovskii function and linear matrix inequalities(LMIs), that followed by the numerical stimulation which is used to verify the effectiveness of the proposed theory.Lastly, we study the Markovian switching topology output coupled CDN, where we use the same sampling method as the last study point. But we consider the noise in channel both in the channel between two different nodes and the channel when we use to construct the state observer. Furthermore, we consider the structure of the observer of CDN, and proposed the distributed state observer, which is based on the real-time topology of the CDN. Then we get the state estimation theory, that is based on the stability theory of Lyapunov-krasovskii,It (?) integral formula and LMIs. Some numerical examples are given at last to illustrate the effectiveness of the theory.