Decentralized Finite-time Control For A Class Of Large-scale Systems

With the rapid development of society and the continuous advancement of communication and network technologies,more and more complex network structures have appeared in the field of daily life,and their characteristics of huge amount of information,cumbersome system structure,and various influencing factors bring many challenges to the research of control theory.Only relying on the methods of earlier control theories can’t obtain satisfactory control results anymore.In this case,the large-scale systems came into being and attracted wide attention from domestic and foreign researchers.Symmetrically interconnected system is a special kind of large-scale system.Due to its symmetrical structure,it’s widely used in the industrial field.Utilizing the similarity of each subsystem can help simplify the system analysis and control synthesis.As a well-targeted,independent and cost-effective control method,decentralized control has extremely high efficiency for symmetrical interconnected system.Up to now,the research results of symmetrical interconnected system mainly based on Lyapunov framework,that is,analyze the steady-state performance of a system as the time approaches to infinity.However,in practice,the transient characteristics of the system in a limited time domain,which called the finite time stability,can make the control effect of the system better.Therefore,it is very important to study the finite time control theory of symmetrically interconnected system.The main content and research results of the paper are as follows:The research results of symmetrically interconnected system and finite time control are sorted out and analyzed,and it is pointed out that there are still many problems in the research of symmetrically interconnected system and finite time control that are worthy of further study.On the basis of the existing research results,utilizing the system structural properties to reduce the complexity of system analysis,The conclusion of the symmetrically interconnected system under the context of Lyapunov’s asymptotic stability is extended to the framework of finite time stability,and the conclusion that the finite time stability of the symmetrically interconnected system can be guaranteed by two lower dimensional systems is obtained.Based on the conclusion,in the case of continuous time,discrete time and uncertain terms,a finite-time decentralized controller design method via state feedback and output feedback is given to stabilized the large-scale system.The solution conditions are transformed to differential matrix inequalities and linear matrix inequalities.The simulation results verify the correctness and reliability of the theory.