Generalized interpolation in control theory (Q1107482)

During the past few years sophisticated mathematical techniques have been introduced in the theoretical engineering branches of circuit and control theory. If one considers the situation just 25 years ago, in which modern linear algebra was for the first time systematically used for systems problems (e.g., in the basic work of Kalman), the methods being used today, ranging from functional analysis to algebraic geometry, indicate how far these subjects have evolved. For example, certain problems in control theory required for their solution new results in operator theory; conversely, certain engineering problems have influenced the research of certain mathematicians and have provided new directions in their work. Our purpose here is not to survey the use of sophisticated mathematics in engineering, but to highlight one specific research area where Nevanlinna-Pick interpolation theory has been used. Explicitly, we would like to discuss the topic of robust control, i.e., system analysis and design in the face of uncertainty.