论文标题
关于具有滞后反馈的线性动态系统的稳定性
On stability of linear dynamic systems with hysteresis feedback
论文作者
论文摘要
考虑了反馈中具有滞后的线性动态系统的稳定性。尽管众所周知的圆圈标准可以证明无内存非线性的绝对稳定性（称为诱饵问题），但多价与速率无关的滞后滞后对反馈系统构成了重大挑战，尤其是为了证明与平衡状态相应设置的融合。顺时针输入输出滞后的耗散行为被考虑在逆转循环时的两个势损失。对于最大（平行四边形）磁滞回路的上边界病例，提供了闭环系统的等效转换。这允许应用绝对稳定性的圆标准。讨论了由于滞后而不变的集合。演示了几个数值示例，包括具有磁滞和一种稳定和一种不稳定的杆配置的反馈控制的双质量谐波振荡器。
The stability of linear dynamic systems with hysteresis in feedback is considered. While the absolute stability for memoryless nonlinearities (known as Lure's problem) can be proved by the well-known circle criterion, the multivalued rate-independent hysteresis poses significant challenges for feedback systems, especially for proof of convergence to an equilibrium state correspondingly set. The dissipative behavior of clockwise input-output hysteresis is considered with two boundary cases of energy losses at reversal cycles. For upper boundary cases of maximal (parallelogram shape) hysteresis loop, an equivalent transformation of the closed-loop system is provided. This allows for the application of the circle criterion of absolute stability. Invariant sets as a consequence of hysteresis are discussed. Several numerical examples are demonstrated, including a feedback-controlled double-mass harmonic oscillator with hysteresis and one stable and one unstable poles configuration.
