A practical method for analyzing the stability of neutral type LTI-time delayed systems
A practical method for analyzing the stability of neutral type LTI-time delayed systems
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DOI：
10.1016/j.automatica.2003.12.010
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发表时间：
2004-05
期刊：
影响因子：
--
通讯作者：
N. Olgaç;R. Sipahi
中科院分区：
文献类型：
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作者：
N. Olgaç;R. Sipahi
提出了一种新的范式，用于评估一般类线性时不变中性时滞系统（LTI-NTDS）的稳定性姿态。接下来的方法，我们将其命名为直接法 (DM)，提供了几个独特的功能： 它以显式且非顺序评估的时间延迟 τ 函数返回系统不稳定特征根的数量。因此，直接法专门创建了 τ 的所有可能的稳定区间。此外，结果表明，该方法本质上验证了 LTI-NTDS τ 稳定性的广泛接受的必要条件。 DM 的核心在于根聚类范式和 Rekasius 变换将超越特征方程映射为等效有理多项式的强度。此外，我们还通过一个例子证明，DM 可以处理 τ=0 时起始姿态不稳定的系统，仅在较高的延迟值下稳定，这在文献中是相当独特的。
A new paradigm is presented for assessing the stability posture of a general class of linear time invariant–neutral time delayed systems (LTI-NTDS). The ensuing method, which we name the direct method (DM), offers several unique features: It returns the number of unstable characteristic roots of the system in an explicit and non-sequentially evaluated function of time delay, τ. Consequently, the direct method creates exclusively all possible stability intervals of τ. Furthermore, it is shown that this method inherently verifies a widely accepted necessary condition for the τ-stabilizability of a LTI-NTDS. In the core of the DM lie a root clustering paradigm and the strength of Rekasius transformation in mapping a transcendental characteristic equation into an equivalent rational polynomial. In addition, we also demonstrate by an example that DM can tackle systems with unstable starting posture for τ=0, only to stabilize for higher values of delay, which is rather unique in the literature.