Generalized KYP Lemma And Its Applications Of 2-D Continuous-Discrete Systems

As one of important research directions of hybrid systems and 2-D systems,2-D continuous-discrete system has been applied in many real engineering areas,such as iterative learning processing,disturbance propagation in vehicle platoons and irriga-tion channels.The dynamics of the systems are related to the behavior of continuous variable as well as behavior of discrete variable.On the other hand,KYP lemma and generalized KYP lemma are important tools for system analysis and control syn-thesis.They establish equivalence between frequency domain inequality(FDI)for a transfer function and a linear matrix inequality(LMI)for its state space realization.This dissertation investigates the generalized KYP lemma of 2-D continuous-discrete systems,and further applies this lemma to considerding a series of the relevant con-trol application problems.The main research works of this dissertation are stated as follows:The stability conditions of 2-D continuous-discrete systems are investigated based on 1-D classical KYP lemma.Furthermore,via frequency partitioning idea,the infinite interval of continuous variable is divided into finite sub-intervals,and in which,1-D generalized KYP lemma is applied to obtain the less conservative stability conditions.Then,subjected to bounded norm uncertainties,the robust stabilization via state feedback of the systems are considered by use of the stability conditions.According to the inner feature of the systems states in the frequency domain,equivalent LMI characterization is given.Then,the generalized KYP lemma for 2-D continuous-discrete systems in any finite rectangular domain is derived via S-procedure.Moreover,the definitions of finite frequency bounded realness and positive realness of the systems are given,and the finite frequency bounded real lemma and finite frequency positive real lemma are investigated as the important corollaries of the generalized KYP lemma.The problems of the finite frequency positive real control of the 2-D continuous-discrete systems are investigated.The finite frequency positive real condition via state feedback is considered combining with stability conditions.With the aid of projection lemma and other technics,the coupled variables are separated and the desired feedback gain matrix is obtained.Numerical examples are given to illustrate the effectiveness of the proposed method.In detail,the systems are positive real in the given finite frequency domain,while they are not anymore when the domain is enlarged.The design of the finite frequency fault detection observer of the 2-D continuous-discrete systems is investigated.The designed observer should guarantee the residual error system be stable,be sensitive to the fault and be robust to the disturbances.The last two conditions are characterized by the inequalities of transfer functions from fault to output and disturbance to output,respectively.The problems of H? fault detection of the 2-D T-S fuzzy systems are investigated.Two kinds of fault detection filters are designed subjecting to different cases.They both can guarantee the residual error systems be stable as well as satisfying a prescribed H?performance level.Numerical examples demonstrate that at the condition of reaching the same optimal H? performance level and feasible region,the two fault detection filters we designed can both detect the fault efficiently.