From differential-algebraic equations to control systems and back

In this talk, we study both linear and nonlinear differential-algebraic equations using geometric method. Firstly, both smooth solutions of DAEs and the problem of inconsistent initial values  will be discussed. Second, we show a novel method called explicitation which attach a class of control systems to a given DAE, then the DAE and control system can be associated  via their equivalence and geometric invariants. This method allows to use classical geometric control theory to solve some DAE problems as linearization, normal forms and finding invariants. Finally, we discuss some problems on the impulsive behavior caused by inconsistent initial value of DAEs.