Asymptotic stability of linear delay differential-algebraic equations with constant coefficients
During the last 20 years, much research has been focused on differential-algebraic equations (DAEs). These systems appear in a wide variety of scientific and engineering applications, including circuit analysis, computer-aided design and real-time simulation of mechanical (multibody) system, power systems, chemical process simulation. On the other hand, much work has also been done in the field of delay differential equations (DDEs). Delay differential equations arise from, for example, real time simulation, where time delays can be introduced by the computer time needed to process the input data. Delays also arise in circuit simulation and power systems, due to, for example, interconnects for computer chips and transmission lines, and in chemical process simulation when modeling pipe flows.
Even though the theory of the analytical and numerical solution of delay differential equations (DDEs) as well as differential-algebraic equations (DAEs) is well understood, the intersection of them, the delay differential-algebraic equations (DDAEs), is still an open object, even for the relatively simple case of linear systems with constant coefficients.
In this talk, we focus on asymptotic stability of linear constant coefficient DDAEs. We first give an introduction about DDAEs and how they are different from both differential-algebraic equations as well as delay differential equations. We then study the canonical form of regular, impulse-free DDAEs of retarded or neutral type, followed by results on conditions for linear constant coefficient DDAEs to be asymptotically stable.