Stability Analysis Of Discrete-time Complex Systems With Impulsive Input Saturation

There are a large number of complex systems in real life,such as urban transporta-tion system,energy system,financial system and so on.Most of the complex systems can be abstracted into the form of complex network,so it is necessary to study and analyze the structure,nature and behavior of complex network more deeply.Because the stability of the system is a prerequisite to ensure the normal operation of the system,the analy-sis of the stability of complex systems has received extensive attention from scholars at home and abroad for a long time.At the same time,as a control method,impulsive con-trol has been widely used in complex networks because of its advantages of small control quantity and low control cost.In addition,in the actual engineering control system,due to the limitation of the physical characteristics of the system and the requirement of safe operation,the saturation phenomenon inevitably exists in the input and output of the sys-tem.Therefore,it is of great theoretical significance to study the stability of discrete-time coupled complex networks with impulsive input saturation.In this paper,the stability of the discrete-time complex system with impulsive input saturation is studied by using the theory of impulsive differential equation,Lyapunov stability theory,convex analysis and other techniques,and the sufficient conditions for the exponential stability of the discrete-time complex system are obtained.Specifically,the main work of this paper includes the following two aspects:（1）The stability of discrete-time systems with impulsive input saturation is studied.In this paper,a general model of discrete-time system with impulsive input saturation is proposed and its stability is analyzed.Combined with Lyapunov stability theory,convex analysis,inequality and other techniques,a method is proposed to analyze the exponential stability of this kind of system.（2）The stability of discrete-time coupled complex networks with impulsive satu-ration input is studied.Firstly,the above methods are applied to the complex network model,and the model of complex network is simplified by means of Kronecker product,convex analysis and auxiliary matrix.Then,the matrix belonging to the M₂set is used to construct the appropriate Lyapunov function,and several sufficient conditions are ob-tained to determine the exponential stability of such a system.Finally,the validity of the conclusion is verified by numerical simulation.