Control And Application For 2-D Time-delay Systems Based On New Inequalities

2-D systems are dynamic processes that depend on changes in two independent states(horizontal and vertical).Many 2-D systems have inherent delays,which will lead to system instability and performance degradation.At the same time,2-D time-delay systems have a wide range of applications in engineering,which makes the study of 2-D time-delay systems of great practical significance.Therefore,many scholars are increasingly concerned about the stability and control of 2-D systems with time-delay.The state of 2-D systems will inevitably change suddenly during operation,switching signals are usually used to adjust the system changes.In addition,nonlinear factors will increase the complexity of the systems and nonlinear systems are closer to the real systems.Therefore,considering the influence of more common mixed time delays in practical systems,the study of control problems for 2-D nonlinear switched systems makes the results more widely used.As a special type of 2-D system,the repetitive system has obtained research results on the control of the repetitive process with time-delay,and the repetitive control technology has also been successfully applied to various practical problems.Therefore,the details are as follows:Firstly,for 2-D discrete systems described by the Fornasini-Marchesini(FM)model,2D Abel lemma is proposed,and 2-D Abel lemma-based finite-sum inequalities are obtained.Applying 2-D Abel lemma-based finite-sum inequalities,the stability analysis,state feedback and dynamic output feedback(DOF)controller design of 2-D FM model system are discussed.New stability criteria with less conservativeness and decision variables as well as a large time-delay upper bound are obtained.The correctness and validity of the results are verified by numerical examples.Secondly,for 2-D nonlinear switching system,considering the mixed time-delay and the instability of all the subsystems,selecting a new Lyapunov functional,using the fast average dwell time switching method,combining the 2-D Abel lemma-based finite-sum inequalities and Jensen inequalities,the stability of the system is studied.A DOF controller is designed to guarantee the stability of the system.The correctness and validity of the obtained results are verified through numerical examples.Finally,for the continuous repetitive system with input delay,a repetitive controller is designed,and the repetitive controller is combined with the initial system to obtain a new closed-loop system.A new integral inequality is applied to study the stability of the new closed-loop system and got a linear matrix inequality(LMI)which makes the system asymptotically stable.The design of the low-pass filter,that is,the method of solving the maximum cut-off frequency,is discussed to improve the performance of the repetitive control system to a certain extent.