Abstract
This paper is concerned with the asymptotic stability of delay differential-algebraic equations. Two stability criteria described by evaluating a corresponding harmonic analytical function on the boundary of a certain region are presented. Stability regions are also presented so as to show the method geometrically. Our results are not reported.
Highlights
Functional differential equations have a wide range of applications in science and engineering
The equation can be expressed as delay differential equation (DDE)
The criteria for the stability of Delay differential-algebraic equations (DDAEs) can be classified into two categories according to their dependence upon the size of delays
Summary
Functional differential equations have a wide range of applications in science and engineering. Perhaps the most natural type of functional differential equation is a “delay differential equation,” that is, differential equations with dependence on the past state. One type of past dependence is that it is carried out through the state variable but not through its derivative. Delay differential-algebraic equations (DDAEs), which have both delay and algebraic constraints, arise frequently in circuit simulation and power system, due to, for example, interconnects for computer chips and transmission lines, and in chemical process simulation when modeling pipe flows. The criteria for the stability of DDAE can be classified into two categories according to their dependence upon the size of delays. Our stability criteria only require the evaluation of a real function on the boundary of a certain region in the complex plane. The stability criteria of DDAEs are presented
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