论文标题
关于具有振荡系数和内核的线性延迟方程的指数稳定性
On exponential stability of linear delay equations with oscillatory coefficients and kernels
论文作者
论文摘要
为非自主标量线性功能微分方程$ \ dot {x}（t）+ \ sum_ {k = 1}^m a_k（t）x（h_k（h_k（t））+ \ int_（t）） t $，$ g（t）\ leq t $，$ a_k（\ cdot）$和内核$ k（\ cdot，\ cdot）$是振荡性的，通常是不连续的功能。这些证明是基于建立溶液的界限，后来使用指数二分法进行线性方程式，表明均匀方程是指数稳定的，或者非均匀方程的方程式具有无界溶液，用于某些有界的右侧。显式测试应用于人口动态模型，例如受控的Hutchinson和Mackey-Glass方程。结果用数值示例说明了结果，并讨论了与已知测试的连接。
New explicit exponential stability conditions are presented for the non-autonomous scalar linear functional differential equation $$ \dot{x}(t)+ \sum_{k=1}^m a_k(t)x(h_k(t))+\int_{g(t)}^t K(t,s) x(s)ds=0, $$ where $h_k(t)\leq t$, $g(t)\leq t$, $a_k(\cdot)$ and the kernel $K(\cdot,\cdot)$ are oscillatory and, generally, discontinuous functions. The proofs are based on establishing boundedness of solutions and later using the exponential dichotomy for linear equations stating that either the homogeneous equation is exponentially stable or a non-homogeneous equation has an unbounded solution for some bounded right-hand side. Explicit tests are applied to models of population dynamics, such as controlled Hutchinson and Mackey-Glass equations. The results are illustrated with numerical examples, and connection to known tests is discussed.
