Event-Triggered Stability Analysis For Linear Systems Based On Sampled-data

Stability analysis of linear systems is an important research direction in the field of control.Nowadays,linear system stability analysis has penetrated into many control fields such as power system,robot control system and industrial network control system.In practical engineering applications,linear systems are often affected by some external uncontrollable factors such as time-delay and network attacks.As a result,its stability research is more complicated.Event-triggered sampling is a control strategy that sets triggering rules based on system state requirements,so it can effectively improve the resource utilization of the system.And it is a popular research method for studying the stability of linear systems.In the network environment,factors such as network attack and communication quality will cause the system to have congestion,packet loss and time delay.So the feedback control of the system cannot achieve the expected effect.By analyzing the internal relationship between the dynamic feedback control effect and the system stability of the linear system,we obtained the sufficient conditions for the system stability under the sampled-data-based event-triggered control strategy.The sampled-data-based event-triggered controller can effectively reduce the number of system sampling in this paper.And,it can also improve the work efficiency of system communication.At the same time,the terminal voltage of the single machine-infinite excitation system has a time delay,and the communication channel of the load frequency control for multi-area power system is often subject to different degrees of network attacks.Therefore,this paper selects the single machine-infinite excitation system and the load frequency control for multi-area power system to conduct example simulation analysis.Specifically,the main research work and contents of this paper are as follows:(1)In order to better study the finite-time stability and finite-time contractive stability of linear time-delay systems,an error function is first given based on sampling control.And according to this error function,we transform the expression of the system.At the same time,we also propose the conditions for event-triggered.Then use the Lyapunov-Razumikhin theorem to simply deal with the time-delay term and combine it with the non-delay term.Furthermore,it obtained the finite-time stability conditions and finite-time contractive stability conditions under the Lyapunov-Razumikhin assumption.By solving by solving the linear matrix inequality,we obtained the designed controller gain for the sampled-data-based event-triggered controller.And it effectively ensures the finite-time stability conditions and finite-time contractive stability.Finally,we give a numerical example and do a simulation.The simulation results prove the effectiveness of the proposed method and controller design.(2)In the actual engineering context,network attacks may have various attack strengths,and we introduced the same event triggering strategy based on sampled data as in the previous chapter.By using Lyapunov stability theory,we obtained a conservative stability condition,when we analyzed the global asymptotic stability of linear systems under multi-mode attack.Simultaneously,we also designed an event-triggered sampling controller,and simulated an example.The simulation results also proved the effectiveness of the proposed method and controller design.(3)In order to make the theoretical research fit for practical application,we model the single machine-infinite excitation system and the load frequency control for multi-area power system.Firstly,according to the application background of the actual system,we modeled the above two system models into linear dynamic equations which are suitable for the study by using suitable linear transformation.And it obtained the suitable system parameter matrices.Then,this paper selected appropriate system parameters,and the experimental simulation is carried out by MATLAB software.In this paper,the correctness of theoretical research and engineering application value have been verified by the analyzing the simulation case.