论文标题
中性型线性系统的渐近特性
Asymptotic properties of neutral type linear systems
论文作者
论文摘要
研究延迟系统的指数稳定性和解决方案估计值$ \ dot {x}（t） - a（t）\ dot {x}（g（t））= \ sum_ {k = 1}^m b_k（t）x（t）x（h_k（t）） H_K $是延迟的参数。稳定性测试适用于具有时变系数和延迟的各种线性中性系统。此外，首次获得了均质和非均匀中性系统解决方案解决方案的明确指数估计。这些不平等不仅是渐近估计值，而且在每个有限段中都是有效的，并评估了解决方案的短期和长期行为。
Exponential stability and solution estimates are investigated for a delay system $$ \dot{x}(t) - A(t)\dot{x}(g(t))=\sum_{k=1}^m B_k(t)x(h_k(t)) $$ of a neutral type, where $A$ and $B_k$ are $n\times n$ bounded matrix functions, and $g, h_k$ are delayed arguments. Stability tests are applicable to a wide class of linear neutral systems with time-varying coefficients and delays. In addition, explicit exponential estimates for solutions of both homogeneous and non-homogeneous neutral systems are obtained for the first time. These inequalities are not just asymptotic estimates, they are valid on every finite segment and evaluate both short- and long-term behaviour of solutions.
