Stability Analysis And Control Of Fractional-order Complex System

After nearly decades of constant study,fractional calculus has been effectively used to separately one by one scopes.Due to fractional calculus is capable of precisely depicting a lot of actual system models and non-classical behavior in actual situation and actuality environment,it has caused a lot of savor of investigators in the scope of system engineering and control.Among them,the stability and stabilization research of fractional nonlinear systems are currently the more mainstream research topics.Stability research problems can be divided into the following difficulties at present:(1)The fractional Routh-Hurwitz criterion method has not been extended to actual fractional complex systems;(2)The research on time-varying delay fractional complex systems is insufficient;(3)In the modeling process of the fractional complex system,the selection of the fractional operator lacks scientific guidance;(4)The high complexity of the structure of the fractional complex system itself causes the structure of the stability constraints to be too complicated.This article will focus on general fractional-order complex system models and some actual fractional-order complex system models,and study several new stability analysis methods.The main work includes:(1)Extend the fractional Routh-Hurwitz criterion method to the actual fractional financial system.research of the dynamics characteristics of the 3D fractional-order financial system and the 4D fractional-order financial system.Then we take the following parameters,such as enterprise requirement resilience,money provide revenue and the delays of various state variables,as the bifurcation point objects.By analyzing the feature equation and the fractional Routh-Hurwitz guidelines,the selection requirements of each bifurcation point are calculated,and the abundant requirements of the asymptotic stability for 3D and 4D fractional-order financial system are derived.In the end,the accurateness for the analysis and derivation part is certificated via computer experiment of 3D and 4D fractional financial systems.(2)Propose a new "WILL"(Wirtinger inequality,Integral Mean Value Theorem—the mean value theorem,Lemma Novel Proposed— the newly proposed functional transformation lemma,Lyapunov function)stability analysis method,which can not only solve The stability problem of fractional-order complex systems which involve time-varying time lag is also valid for the stability problems of more complex fractional-order complex systems with time-varying delays.In addition,this method is less conservative.Then apply this method to different actual time-varying time-delay fractional-order nonlinear systems which involve time lag,envelope the fractional gene control system and the fractional HIV-1 infectious disease system,and derive the corresponding sufficient stability conditions respectively,so as to reflect this method has very obvious generalized conclusion.In the end,the accurateness for the analysis and derivation part is certificated via computer experiment.(3)For the purpose of settling the puzzle of the shortage of rationality direction in the selection of fractional operators during modeling procedure of fractional complex systems,our article in-depth researches the connection among fractional operators and fractional complex systems.First,by studying the gamma function with the fractional operator as a variable,some new properties of the gamma function with the fractional operator as the variable are put forward.Then linking with the "WILL" stability analysis method which is put forward by us,the influence of the change of fractional-order operator on the fractional-order complex system is explained in detail,so as to make up for a major deficiency in the modeling process of the fractional complex system.In the end,the accurateness for the analysis and derivation part is certificated via computer experiment.(4)For the purpose of settling the puzzle of redundant and involuted asymptotic stability constraints caused by the intricate construction of the fractional composite systems,our article puts forward some novel means extended from the Lyapunov function method,Lyapunov-Like function method and Lyapunov-M matrix method.The Lyapunov-Like function method mainly converts the fractional-order problem into an integer-order problem that is easier to analyze and calculate,thereby greatly reducing the complexity of the problem,but this method can only handle the case of no time delay.The vector Lyapunov-M matrix method can settle both the stability puzzle of the situation without time delay,and the stability puzzle of the situation with time delay,and it also has the advantages of fewer constraints and simple structure.advantage.In addition,based on these two new methods,we research the asymptotic stabilization control for the fractional composite system.