Stability Analysis And Controller Design For Variable Period Sampling Control Systems

The data sampling phenomenon has been widely used in digital control systems and networked control systems,and it has attracted wide attention.The sampling control systems are generally divided into fixed period sampling control systems and variable period sampling control systems,and the variable period sampling control systems are in line with the actual situation.In the practical application of sampling control systems,the large system sampling interval means loose operating conditions,such as load limits and computational burden,which can save the cost of sampling equipment.Therefore,it is important to obtain the maximum allowable sampling interval under the condition of the stability of the sampling control systems.This also explains why the problem of system stability analysis related to the maximum allowable sampling interval in sampling control systems has been a topic of special interest to many researchers in recent years.Therefore,this paper studies the stability of the sampling control systems through the input delay method and the Lyapunov-like functional method,and carries on the stability analysis and controller design of the nonlinear sampling control systems.The main contents of this paper are as follows:(1)Stability analysis of variable period sampling control systems based on input delay method: Firstly,we construct the system mode,and the closed-loop control system is constructed by using the input delay method to process the system model.Secondly,by constructing a Lyapunov functional and using the Jensen’s inequality,we prove the proposed stability criterion.Finally,numerical examples and simulation examples are used to verify the final results.(2)Stability analysis of variable period sampling control systems based on the Lyapunov-like functional method: Firstly,we construct a system model,and perform input sampling and state feedback to construct a closed-loop control system.Then,by constructing the Lyapunov-like functional,we derive the stability criterion of the system by applying the lemma and inequality techniques introduced.Finally,we give numerical examples and simulation examples to verify the final results.(3)Aiming at the stability analysis and controller design of T-S fuzzy variable periodic sampling control systems: Firstly,we construct the T-S fuzzy system model through the T-S fuzzy method,and then by constructing the Lyapunov-like functional,using inequality to shrink the derivative of the Lyapunov-like functional,derive a less conservative stability criterion.A effective controller design scheme is given.Finally,the validity of the theorem is verified by simulation examples.In this paper,the input delay method and the Lyapunov-like functional method are used to analyze the stability of linear sampling control systems,and the Lyapunov-like functional method is used to analyze stability of nonlinear sampling control systems and design the controller.The stability criterion with less conservative properties is derived by introducing the augmented matrix and applying different matrix inequalities.