Transient Performance Analysis For Discrete 2-D Systems

The study of 2-D(Two-Dimensional)systems has attracted considerable attention and an extensive progress has been made in this fields.In particular,system control theory and math-ematical methods in control theory have been promoted along with the deeply development of stability theory.Both Lyapunov stability(LS)and bounded-input bounded-output stability(BI-BO)are the primary components of the system stability theory;and are also the foundation in the most of the system control synthesis issues.The system's state and the controlled output signal are characterized by LS and BIBO respectively in a large enough space(in principle,the entire first quadrant).However,for some practical applications,systems only operate over a finite region(i.e.some finite region in the first quadrant);in this case,the transient performance of systems plays an important role.Obviously,it is not reasonable to reflect the behavior char-acteristics of the system state and the controlled output during a finite region with the help of LS and BIBO theory.In 1-D systems,finite-time stability and input-output finite-time stability are regarded as effective approaches when considering transient performance of state and out-put signals.In this paper,based on the existing work in 1-D systems,it formulates the analysis methods and control theory for the transient performance of discrete 2-D systems.The main work and research results are described in the following aspects:1.For discrete 2-D Fornasini-Marchesini second(FM?)models,the concepts of finite-region stability and finite-region boundedness are presented,and then,we establish sufficient criteria and linear matrix inequalities(LMIs)conditions.On the basis of this,finite-region stabilization issues is considered,and the corresponding results are formulated.2.Finite-region stability and boundedness issues are considered for discrete 2-D Roesser models.Through the alternative mathematical inductive method,the special iterative formulas are established,and then the solvable LMIs criteria are obtained which guarantee finite-region stability and boundedness of the 2-D systems.Furthermore,finite-region stabilization problem is also analyzed,and the corresponding criteria are presented.3.For discrete 2-D FM? models,the concept of input-output finite-region stability is in-troduced firstly,and the sufficient criterion and LMIs conditions are studied in detail.Then,by designing appropriate state feedback controllers,the input-output finite-region stabilization is investigated for the corresponding closed-loop systems,and the criteria are presented accord-ingly.4.In the discrete 2-D Roesser models,the concept of input-output finite-region stability is introduced,and the criteria and LMIs conditions are established for input-output finite-region stability.By designing an appropriate state feedback controller,input-output finite-region sta-bilization of the closed loop system is realized,and the corresponding sufficient conditions are obtained.