Normal Robust Filter Design with Performance Constraints
Date Issued
2006
Date
2006
Author(s)
Lee, Ching-Min
DOI
en-US
Abstract
This dissertation studies the robust H∞ filtering problems with performance constraints. Not only the H∞ performance index is considered for filter design, but also various constraints with respect to other filtering performance requirements are posed for different systems. A general performance specification of filtering problems in signal processing and communication systems is the filter output time-domain response envelope constraints. It is especially of theoretical interest and practical importance for MIMO systems with uncertainties, since coupling effects can be accommodated. Another general performance specification often concerned is about the pole locations of filter systems. Unlike the time-domain envelope constraints, setting pole location constraints is an indirect approach based on the knowledge of system responses and pole locations, but it is widely adopted by
experienced system designers. In contrast to control system
design problems, in filtering problems only the filter, not the overall system, pole locations may be selected, and systems with unstable poles need to be treated separately. Here both systems described by normal state-space models as well as singular state-space models are considered. This is mandatory because in some cases normal state-space models can not express the impulsive characteristic as the singular systems, especially when systems are perturbed.
This dissertation begins by considering filtering problems with the time-domain envelope constraints, and proposes direct methods allowing one to design filters with the channel coupling cancellation capability for the MIMO systems. Then, the D-stability constraint for the filter is considered, enabling filter designers to shape the filter characteristics in a flexible fashion. Subsequently, filtering problems for singular systems with uncertainties are studied to compare the performance with normal and singular filters. In the development process a normal transformation that transfers singular system models with uncertainty to normal system models is proposed. Finally, a deeper exploration is made by letting all system matrices to contain uncertainties in the singular system models, as well as letting systems to have unstable poles. A feature of this research is the use of LMI techniques in both analysis and synthesis problems, so all derived method are easy to implement and computationally efficient.
Subjects
封套條件
濾波器設計
線性矩陣不等式
π分配理論
區域極點配置
受限系統等效性
強健性
奇異系統
envelope constraints
filter design
linear matrix inequality
π-sharing theory
regional pole placement
restricted system equivalence
robustness
singular systems
Type
thesis
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