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# Differential-algebraic equations with time-delay: solvability analysis and control

Phi Ha:

During the last 20 years, much research has been focused on differential-algebraic equations (DAEs). These systems appear in a wide variety of scientic 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 dierential 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 coecients.

In this talk, we first address the solvability analysis of linear delay differential algebraic equations by proposing an algorithm that explicitly reads off underlying delay differential equations, and also all hidden constraints. In the remaining part of the talk, we discuss the problem of controlling DAEs by time-delayed feedback, followed by several illustrated examples.