Finite Frequency H_∞ Filtering Analysis And Synthesis Of Time-delay Systems

Filtering or state estimation is using the external measured signal to estimatethe unmeasurable signal, which is one of the fundamental problems in control theory,signal processing and other areas. Due to the necessity of both precisely known sta-tistical data of noise and the system state space model, the classic Kalman filteringoften encounters the problem of poor robustness in practical engineering application-s. Hence, over the past decades, many scholars have been studying robust filteringunder nongaussian noise disturbance input, among which, H∞filtering is one ofthe most widely concerned problems. It is worth noting that, after twenty yearsdevelopment, H∞filtering theory is mostly based on the standard H∞performanceindex, which requires that the filtering error system has the same noise disturbanceattenuation level over the entire frequency domain. Since this index does not makefull use of the frequency information of the noise, it is difficult for standard H∞filters to achieve the ideal performance requirements. In addition, time-delay in-evitably exists in many practical dynamic systems; especially with the developmentof network technologies, time-delay often becomes the key factor that affects systemperformances. With the establishment of the generalized KYP lemma, the prob-lems of analysis and synthesis of finite frequency (FF) H∞filtering for time-delaysystems have been the research hotspots in recent years in the field of H∞filteringtheory. By comprehensively applying the Lyapunov stability theory and the gen-eralized KYP lemma, this thesis in deep investigates the problems of analysis ofthe FF H∞performance, design of FF H∞filters and so on for continuous- anddiscrete-time time-delay systems, and in the framework of linear matrix inequality(LMI), proposes the analysis and synthesis methods for FF H∞filters.First, this thesis summarizes the main achievements in the research field ofH∞filtering theory for time-delay systems, and points out the shortages of thecurrent main achievements of FF H∞filtering threefold: 1) the majority of resultsare independent of delay, only able to handle quite limited time-delay systems; 2)they have not made full use of the latest techniques that reduce the conservatismof results for time-delay systems, such as delay-partitioning; 3) all the results are derived from the perspective of the transfer function and it is hard to further promotethis method in the aspect of conservatism reduction. Based on these analysis, theproblem of analyzing the FF H∞performance for continuous- and discrete-timelinear time-invariant (LTI) systems with constant state delay is studied, and newFF bounded real lemmas (BRLs) for time-delay systems are proposed. Moreover,time-domain method and frequency-domain method for the proof of the new BRLsare respectively provided.Second, based on the proposed BRLs, the problems of FF H∞filtering forcontinuous- and discrete-time LTI systems with constant state delay are researched,and by virtue of projection lemma, LMI-based delay-dependent and -independentmethods are proposed for the design of FF H∞filters. Theoretical analysis andsimulation results verify that the proposed filter design methods are less conservativethan the existing ones in the literature.Third, as the extension of the problem of FF H∞filtering for time-delay system-s, the thesis still investigates the problem of robust FF H∞filtering for 2D Roessersystems with polyhedron parameter uncertainty, a special class of time-delay sys-tems. By combining the existing generalized KYP lemma for 2D Roesser systemswith projection lemma, an FF H∞filter design method is obtained. Through theuse of a more general linearization procedure, the existing filter design methods for2D systems are only special cases of the proposed one.