This paper solves the problem of boundary feedback stabilization of a class of coupled ordinary differential equations_hyperbolic equations with boundary, trace, and integral nonlocal terms. Using the backstepping approach, the controller is designed by formulating an integral operator, whose kernel is required to satisfy a coupled hyperbolic partial integral differential equation. By applying the method of successive approximations, the kernel's well-posedness is given. We prove the exponential stability of the origin of the system in a suitable Hilbert space. Moreover, a wave system with nonlocal terms is stabilized by applying the above result.

中文翻译：

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一类非局部项耦合双曲方程的边界反馈镇定


本文解决了一类带有边界、迹和积分非局部项的耦合常微分方程_双曲方程的边界反馈镇定问题。采用反步法，通过制定积分算子来设计控制器，要求其核满足耦合双曲偏积分微分方程。通过应用逐次逼近的方法，给出了核的适定性。我们证明了系统原点在合适的希尔伯特空间中的指数稳定性。此外，通过应用上述结果，具有非局部项的波动系统得以稳定。