The Stability Analysis Of Two Class Of Discrete-time Coupled Systems

During the past decades,the discrete-time coupled systems on networks(DTCSN)have received considerable attention,due to their extensive applications developed in physics,biology,neural network,engineering and other areas.Meanwhile,the focus of the study is the stability of DTCSN.With the deepening of research,we introduce time-varying delays and random disturbance into DTCSN in order to more accurately describe the natural phenomena,and consider their influence on DTCSN stability.Lyapunov stability theorem is the common method for analyzing global stability for DTCSN.However,the application of this method has great difficulty.Due to some complex coupled systems,constructing a global Lyapunov function is a complex and challenging work.In this dissertation,combining graph theory and Lyapunov method,we systematically construct a global Lyapunov function to obtain the stabilities of the two classes of DTCSN.In the first part of this dissertation,based on graph theory and Lyapunov method,the global stability of DTCSN with time-varying delays is analyzed.The construction of global Lyapunov function for the DTCSN with time-varying delay is given,and then some novel sufficient criteria of stability are obtained.Furthermore,the theoretical results are applied to a network of discrete-time coupled oscillators.Finally,a simulation is given to illustrate the effectiveness of the theoretical results.In the second part of this dissertation,the global asymptotic stability in the mean square sense of the discrete-time stochastic coupled systems with time-varying delays have been analyzed.Combining graph theory and Lyapunov method,a systematic method is given for constructing a global Lyapunov function for the discrete-time stochastic coupled systems with time-varying delays.Some novel sufficient criteria of global stability for the discrete-time stochastic coupled systems with time-varying delays are obtained.The theoretical results of previous section will be extended to the discrete-time stochastic coupled systems with time-varying delays.Finally,a numerical example is given to illustrate the effectiveness of the theoretical results.