One of the most important contributions of robust control theory has been the devel opment of a new framework for the design and analysis of feedback systems satisfying mixed time-frequency specifications. This framework is given by the Linear Matrix Inequality (LMI) approach where design and analysis problems are posed as convex optimization problems subject to affine matrix constraints. Most of the focus in this area has been on continuous-time systems design with very few results for discretetime systems. One of the main contributions of this work is the development and implementation of a MATLAB toolbox for discrete-time controller design using the LMI approach. Another important contribution is the development of a new linear matrix inequality for peak-to-peak gain minimization that allows the use of projec tion formulas for l1-design. In order to illustrate the advantages and effectiveness of the LMI framework to multiobjective design problems it was applied to design a noise-shaping feedback coder. This nonlinear circuit is an important component of (Sigma) - (Delta) modulators. This work shows that a robust control approach based on LMIs provides a rigorous framework for the systematic analysis and design of these coders in contrast to existing ad hoc methods used traditionally for such designs.

Library of Congress Subject Headings

Digital control systems; Signal processing--Mathematics; Feedback control systems; Discrete-time systems; Matrix inequalities

Publication Date


Document Type


Student Type


Degree Name

Computer Engineering (MS)

Department, Program, or Center

Computer Engineering (KGCOE)


Juan Cockburn

Advisor/Committee Member

Andreas Savakis

Advisor/Committee Member

Greg Semeraro


Physical copy available from RIT's Wallace Library at TJ223.M53 O247 2004


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