Control And Filtering Of 2-D Discrete Systems With Time-varying Delay Based On FM Model

Two-dimensional(2-D)systems play an important role in iterative learning control,multi-dimensional digital filters and other disciplines and engineering fields.Many scholars had conducted extensive researches on 2-D discrete systems and achieved many results.In many practical systems,time delay is inevitable,and time delay often changes with time,which is called time-varying delay.In order to better solve practical problems,it is necessary to analyze the stability of the system more from the theoretical perspective,so as to reduce the adverse effects of time-varying delay on the stability and performance of dynamic systems.Therefore,based on the 2-D discrete system with time-varying delay described by the Fornasini-Marchesini(FM)model,the following research works are done:Firstly,the delay-variation-dependent stability problem for 2-D discrete systems with delays is studied.The created Lyapunov-Krasovskii Functionals(LKFs)consider the introduction of time-delay correlation matrices into the quadratic and single-term summation terms,taking into account more state information.Simultaneously,the augmented vector matrices are introduced into the single sum term to study the stability of the system.Finite sum terms in the differential process of LKFs are handled in terms of multiple auxiliary function inequalities and mutually convex combinatorial inequalities.Then,new stability criterion is derived for 2-D discrete systems with time-varying delay.Finally,the effectiveness and superiority of the present design method are verified by comparing with the existing results.Secondly,the state feedback control problem of 2-D discrete time-delay system with multiple input constraints is studied by integrating nonlinear disturbance factors.The multiple input constraints include nested nonlinearity with slope limiting,quantization,saturation and actuator overflow.By limiting the inherent nonlinearity of the system to satisfying the one-side Lipschitz conditions and quadratic inner bounded conditions,the finite sum terms in the difference process of LKFs are treated according to the 2-D weighted summing inequality,an asymptotic stability criterion is established for the 2-D discrete time-delay system.System stability is ensured by designing the state feedback controller.Then,the results are applied to examples of thermal processes to illustrate effectiveness and practicality.Finally,based on the 2-D discrete time-varying delay system with missing measurements and nonlinear interference factors described by the FM model,the time-varying delay stability and H∞ filtering problems of the system are studied.In the selected LKF s,quadratic terms dependent on the squared of the time delay are introduced,the system stability criterion based on the linear matrix inequality(LMI)is obtained by the convex method.Then the filter is designed.The feasibility of LMIs verifies that the filter error system is asymptotically stable,and ensure that the system has H∞ performance Υ.Furthermore,the Matlab toolbox is used to verify the effectiveness of the stationary random field filtering design.