Consensus Analysis Of Fractional-order Nonlinear Multi-agent Systems With Delays

In the past few decades,cooperative control of multi-agent has attracted interest of scholars for its extensive applications in various fields.As the most basic and significant problem in cooperative control of multi-agent,consensus problem has become one of the current research hotspots.Compared with the integer derivative,the fractional-order derivative can more accurately describe complex phenomena in the real world.Therefore,this paper will investigate consensus problem of fractional-order nonlinear multi-agent systems with delays through fractional-order Razumikhin method,the main contents are as follows:1.The consensus problem of fractional-order nonlinear multi-agent systems with dis-crete delay is studied.Because the main tool for studying consensus is stability theory,so this paper turns the consensus problem of multi-agent state systems into stability problem of error systems.Then,by constructing simple quadratic Lyapunov functions,utilizing modified fractional-order Razumikhin theorem,graph the.ory,methods and techniques of analysis,the linear matrix inequality conditions for the system to achieve consensus axe obtained,the linear matrix inequality conditions are easier to verify.2.The consensus problem of fractional-order nonlinear multi-agent systems with distributed and input delays is investigated,and the major research method is similar to research approach of consensus of fractional-order systems with discrete delay.However,in the treatment of nonlinear terms,the traditional Lipschitz condition is reduced to QUAD condition.This makes the results more widely applicable.There are two main innovations in this paper.First,the innovation of research meth-ods.The multi-agent systems studied in this papaer are modelded by Caputo fractional-order delayed equations,because the Caputo derivative does not satisfy the composition properties of operators,so it is very difficult to construct a suitable Lyapunov function to solve the stability problem.However,in this paper,a simple quadratic Lyapunov func-tion is constructed based on fractional-order Razumikhin method to study the stability problem.Second,the innovation of research object.In the fourth chapter,we study the consensus of fractional-order multi-agent systems with distributed delay,the correspond-ing topology of systems is a weighted directed graph,the weighted digraph can better describe the actual system.The consensus of fractional-order systems with distributed delay has not been studied.