广义Jensen不等式及其在具有无限时间 horizon 分布延迟系统稳定性分析中的应用
Generalized Jensen Inequalities with Application to Stability Analysis of Systems with Distributed Delays over Infinite Time-Horizons
AI总结：
本文提出广义积分不等式及其双积分扩展，用于改进具有伽马分布延迟的线性连续时间系统稳定性结果，并提供扩展的Jensen求和不等式以改善具有泊松分布延迟的线性离散时间系统稳定性条件。
摘要：
Jensen不等式已被认可为处理时滞系统稳定性的强大工具。最近，一种包含Jensen不等式的不等式被提出用于有限时滞系统的稳定性分析。本文首先提出了广义积分不等式及其双积分扩展。展示了这些不等式如何应用于改进具有伽马分布延迟的线性连续时间系统的稳定性结果。然后，对于离散时间对应物，我们提供了一个扩展的Jensen求和不等式，具有无限序列，这导致了具有泊松分布延迟的线性离散时间系统的更不保守的稳定性条件。通过示例展示了由于引入的广义不等式获得的改进。
英文摘要：
The Jensen inequality has been recognized as a powerful tool to deal with the stability of time-delay systems. Recently, a new inequality that encompasses the Jensen inequality was proposed for the stability analysis of systems with finite delays. In this paper, we first present a generalized integral inequality and its double integral extension. It is shown how these inequalities can be applied to improve the stability result for linear continuous-time systems with gamma-distributed delays. Then, for the discrete-time counterpart we provide an extended Jensen summation inequality with infinite sequences, which leads to less conservative stability conditions for linear discrete-time systems with poisson-distributed delays. The improvements obtained thanks to the introduced generalized inequalities are demonstrated by examples.
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