PI's research interests are in developing theory to describe those properties of linear feedback systems that are relevant to design. Of particular interest is the way in which the structure of a system to be controlled limits the performance and robustness properties achievable through feedback design. In the scalar case, plants with nonminimum phase zeros, unstable poles, and time delays cause design difficulty. These properties can also appear in multivariable systems. However, in this context they are less well understood, and seek to develop a mathematical framework within which to explore their properties. Multivariable systems can also possess properties having no analogue in the scalar case. Among these are directionality properties due to loop interactions and to plant ill-conditioning. He seeks to understand these properties and the design tradeoffs and limitations that they impose. He then plans to incorporate this knowledge into various existing design methodologies as well as to develop new methodologies. His ultimate research goal is to understand feedback system properties sufficiently well that rules of thumb may be developed to aid in design. This task will involve both development of the necessary theory, as well as a substantial effort to translate that theory into the language of the practicing engineer.
