Controllability and Observability of Sylvester Differential Algebraic Equations

Differential Algebraic Equations (DAEs) arise naturally as governing equations for systems in chemical, electrical, and mechanical engineering as well as biological and economic models. Therefore, the analysis of DAEs plays an important role in applied mathematics. Dr. Wu provides an overview of DAEs in this talk, followed by the latest results on the first-order Sylvester type of differential algebraic systems with input and output structures incorporated in the system. Dr. Wu will first present a closed form representation for the general solution of matrix Sylvester DAEs in terms of the fundamental matrix solutions of one-sided subsystems. The result is then used to derive a set of necessary and sufficient conditions for the complete controllability and complete observability of the Sylvester systems. Dr. Wu will introduce most background materials in the presentation, so that this talk will be accessible to students.

For interested students, Dr. Wu will follow his presentation with information on the Master degree in Mathematics and Statistics offered in the Department of Mathematical Sciences at Georgia Southern University. The Mathematics Department offers graduate assistantships to most students accepted to the MS program. The assistantship ranges between $8000 and $10,000 for about 12-15 hours workload per week. The primary duty of graduate teaching assistant is to teach recitation sessions for calculus I and II. Work, earn experience and an Master degree close to home!