Mathematical Sciences: Algebraic Methods in Systems Theory

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9300805 Rosenthal This project addresses a number of issues in systems theory, interpolation theory and coding theory, all of which involve algebraic properties of the class of all autoregressive systems of a bounded degree. The main objectives of the research are improved methods for the design of stabilizing dynamic feedback compensators, a better understanding of the interplay between issues of robustness and topological properties of the space of transfer functions, and new methods for constructing classes of convolutional codes with a low complexity and a large free distance. Many real world systems may be mathematically modeled by so- called linear systems. Two examples of a linear system are dynamic feedback compensators, which are widely used in the design of feedback controllers, and convolutional encoders and decoders, which are implemented in many data transmission schemes. It is the goal of this project to develop a mathematical theory which will lead to improved design techniques for feedback controllers of various types as well as more efficient convolutional encoders and decoders. ***