| 2-D system refers to a dynamic system which depends on two independent state variables(horizontal and vertical).2-D system has been widely applied in many fields,such as image pro-cessing,multi-dimensional signal processing,wireless signal communication,and water heating.Compared with 1-D system,the dynamical properties of 2-D system are much more compli-cated.In addition,time delay is an important factor to influence the system performance.In this paper,we focus on the problem of 2-D time delay system's performance analysis in finite frequency domain.Based on that,the feedback control problem of 2-D time-delay system in finite frequency domain and the designing of fault diagnosis filter are also studied.The article includes four chapters.In Chapter 1,we introduce the research background of this article.In Chapter 2.we study the performance analysis problem of 2-D time delay system in finite frequency domain.Based on GKYP lemma,in the form of LMI,sufficient condition of 2-D time delay system satisfies the desired performance in finite frequency domain is given.In Chapter 3,we explore state feedback control problem of 2-D time delay system in finite frequency domain.Firstly,closed-loop system satisfies H_? performance index's sufficient condition in the finite frequency is presented,then,a series of contract transformation separates the gain matrix K from the parameter matrix,then sufficient condition and specific design methods of state feedback controller are given.Finally,the validity of the design method are demonstrated by numerical examples.In Chapter 4.we investigate the fault detection filter problem of 2-D time delay system in the finite frequency.Firstly,designing the fault detection filter system ensures the error system being H_,H_? performances index and asymptotically stable in linear matrix inequalities.Then,the fault detection system is judged by the observation of the residual.Finally,the validity of the design method is demonstrated by a numerical example. |
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