Research On Guaranteed Cost Control Of Uncertain Nonlinear Two-Dimensional Systems

Two-dimensional systems have the typical characteristics of multi-dimensional systems and have been widely used in the fields of process control,image processing,and multi-dimensional signal filtering.In practical control systems of which nonlinearities is ubiquitous.Moreover,for various reasons,the parameters of systems will be uncertain,and it is very necessary to consider the uncertainties of the systems.In addition,input saturation characteristics are also widely present in real-world control systems.If these problems are not effectively solved,they will pose a great threat to system performance and stability,therefore,considering these problems this article focuses on the guaranteed cost control problem of uncertain nonlinear two-dimensional discrete systems based on Roesser model.The specific research content is as follow:(1)Under the network environment,the event-triggered guaranteed cost control problem of uncertain nonlinear two-dimensional discrete systems is studied.The event-triggered condition is designed for a two-dimensional discrete system with norm bounded uncertainties and sector nonlinearity.Based on the Lyapunov stability theory combined with event triggering conditions,the conditions are given for closed-loop systems is asymptotic stability and guaranteed cost control is existing.What's more,the conditions are transformed into linear matrix inequalities(LMI),which give design method of guaranteed cost controller.Finally,the validity of the results is verified by numerical simulation examples.(2)For the uncertain nonlinear two-dimensional discrete systems,the problem of guaranteed cost control with input saturation is studied.For the input saturation characteristics,the convex hull description method is used to obtain a less conservative result.Based on the Lyapunov stability theory,the sufficient conditions are given for which the asymptotic stability of the closed-loop system and the existence of guaranteed cost control are presented for the two-dimensional discrete systems with norm-bounded uncertainties and sector nonlinearities.The condition is transformed into the LMI form,and the design method of the guaranteed cost controller is given and verified by numerical simulation.(3)Based on the results of(2),the problem of guaranteed cost control of the system is further studied.Consider the external disturbance of the systems and analyze the H_?performance of systems.According to the Lyapunov stability theory,the LMI condition for the guaranteed cost control of the system with input saturation and external disturbance is given for the uncertain nonlinear two-dimensional discrete system.At the same time,the closed-loop system is guaranteed to be asymptotically stable.The relevant parameters of the controller are solved by MATLAB LMI Toolbox,and simulation verification effectiveness.