Mathematical Sciences: T+H*H Operators in Linear-Quadratic and H-Infinity Problems

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This project focuses on some issues arising in the mathematical theory of control problems for linear systems. The central theme of this project is an operator of the form T + H*H where T is Toeplitz and H is Hankel. The motivation is two-fold. First, as previously shown by the principal investigator, the linear quadratic optimal control problem has a T + H*H operator that reveals a lot of structure not identifiable by conventional means. Secondly, as shown by the investigator, the H - infinity design problem alsdo involves a T + H*H operator, the largest eigenvalue of which provides the so called achievable feedback performance, a critical parameter. As such, this operator reveals a strange connection between the linear quadratic problem and H - infinity problems. This connection will be investigated along with its spectral and computational aspects. This research is part of a larger effort conducted in this country by theoretical engineers and mathematicians to develop a unified design methodology for linear control systems with robustness requirements on the design. This research combines fileds such as systems engineering and operator theory in mathematics.