Sampled-data-based Stability And Robust Performance Analysis For Systems Interconnected Over An Undirected Graph

Systems interconnected over an undirected graph are such a kind of large-scale system that the topological relationship between subsystems can be characterized by an undirected graph.It utilizes a set to characterize the interconnection signals between the subsystems,which can reflect many interconnected systems in the real world well.Modern control and communication technologies mostly employ sampled-data based digital devices and shared networks as the carriers of signal processing and transmission,in order to deal with the problems of large-scale systems including the large number of subsystems and wide spatial distribution.If these technologies are introduced into the systems interconnected over an undirected graph,the flexibility of system design and the convenience of system maintenance can be improved.However,the existing analysis methods for purely continuous-time or purely discrete-time systems interconnected over an undirected graph are not suitable for the analysis of such interconnected system based on sampled-data control or communication.Thus,investigating the performance of such interconnected system based on sampled data is of theoretical significance and application value.This dissertation mainly studies the stability and robust performance for systems interconnected over an undirected graph based on sampled data.The main work of this dissertation includes:(1)For the case of the ideal interconnection among the subsystems,the stability analysis of the interconnected system with sampled-data control is considered.At first,we analyze the stability of interconnected system with sampled-data control and actuator saturation.By employing improved Lyapunov approach,we obtain sufficient conditions to guarantee the regional stability of the interconnected system,and give a rough estimate of the attraction domain by the obtained conditions.Then,we talk about the stability of the interconnected system with state quantized sampled-data control.By using the input-delay approach,we derive linear matrix inequality(LMI)conditions to guarantee the stability of the considered system,which only depend on the subsystem parameters,quantization parameters and the sampling interval.Based on these LMI conditions,a grid-based algorithm is given to get optimal sampling interval for each subsystem.At last,numerical examples show the effectiveness of the obtained results.(2)For the case that the communication among uncertain subsystems is affected by the network transmission protocol and asynchronous aperiodic sampling,the robust performance analysis of the interconnected uncertain system based on sampled-data communication is investigated.Firstly,a unified framework model of hybrid system is used to incorporate the discrete dynamic of the network and the continuous dynamic of the considered system.Then,a general lemma is provided to guarantee the robust performance of the hybrid system.A hybrid Lyapunov function is constructed to meet the requirement of this lemma,and sufficient conditions are obtained to ensure the robust performance of the interconnected system,which depend only on the parameters of individual subsystem and local network.The bound of the maximal allowable sampling interval for each local network is given by an explicit formula.Finally,the derived conditions are verified by an example of two-area power system.(3)For the case that the communication among time-delay subsystems is affected by the network transmission protocol and synchronous aperiodic sampling,the problem of stability and L2 stability of the interconnected time-delay system is addressed.Firstly,by eliminating the interconnected variables,the considered interconnected system with state-delay and communication constraints including aperiodic sampling interval and transmission protocol is reformulated as the model of hybrid system with memory.Then,using the newly developed stability theory of hybrid system with memory,a general hybrid L-K functional is constructed.Based on this functional,tractable conditions are derived to reveal the relationship between the stability of the considered interconnected system and the networked parameters as well as the delays.A formula is provided to calculate the bound of the maximal allowable sampling interval.Finally,the validity of the main results are illustrated by two examples.(4)For the case of the nonideal interconnection among the subsystems,the H∞ performance analysis of the interconnected system based on event-triggered sampled-data control is studied.Firstly,a lemma is given to verify the well-posedness of the systems interconnected over an undirected graph with nonideal interconnection.Based on this lemma,suitable auxiliary variables are introduced to transform the considered system into a error-dependent time-delay system.Then,an L-K functional is constructed to obtain sufficient LMI conditions,which can check the H∞ performance of the considered interconnected system using the matrix parameters of individual subsystem directly.With the help of Finsler lemma and weighted relaxation matrix method,the co-design method of event-triggered parameter and control gain is given.Finally,two examples are used to illustrate the validity of the derived methods.