On the links between limit characteristic zeros and stability properties of linear time-invariant systems with point delays and their delay-free counterparts

[摘要] We investigate the relationships between the infinitely manycharacteristic zeros (or modes) of linear systemssubject to point delays and their delay-free counterparts basedon algebraic results and theory of analytic functions.The cases when the delay tends to zero or to infinity areemphasized in the study. It is found that when the delay isarbitrarily small, infinitely many of those zeros are located inthe stable region with arbitrarily large modulus, while theircontribution to the system dynamics becomes irrelevant. Theremaining finite characteristic zeros converge to those of thedelay-free nominal system. When the delay tends to infinity,infinitely many zeros are close to the origin. Furthermore, thereexist two auxiliary delay-free systems which describe therelevant dynamics in both cases for zero and infinite delays. Themaintenance of the delay-free system stability in the presence ofsufficiently small delayed dynamics is also discussed inlight ofH∞-theory. The main mathematicalarguments used to derive the results are based on the theory ofanalytic functions.

[学科分类] 应用数学