Stability Criteria for Second-Order Dynamical Systems With Time Lag
Stability Criteria for Second-Order Dynamical Systems With Time Lag
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DOI：
10.1115/1.3624967
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发表时间：
1966-03
期刊：
影响因子：
--
通讯作者：
C. Hsu;S. J. Bhatt
中科院分区：
文献类型：
--
作者：
C. Hsu;S. J. Bhatt
利用指数多项式零点上的庞特雅金定理研究了具有时滞的二阶动力系统的稳定性。时滞项可以涉及位移、速度或加速度。还考虑具有负阻尼系数和/或负弹簧常数的系统。结果表明，适当强度和适当延迟的延迟反馈信号能够稳定具有负阻尼和/或负弹簧常数的动态系统。还发现，文献[2]中针对阻尼系数为正且弹簧常数非负的限制情况给出的一些早期结果是有缺陷的。这里获得的稳定性标准用不等式来表示，这些不等式对系统参数施加了上限和下限。
Stability of second-order dynamical systems with time lag is investigated by using Pontrjagin’s theorems on the zeros of exponential polynomials. The time-lag term may involve the displacement, the velocity, or the acceleration. Systems with negative damping coefficient and/or negative spring constants are also considered. It is shown that a delayed feedback signal of proper strength and proper delay is capable of stabilizing such dynamical systems with negative damping and/or negative spring constants. It is also found that some earlier results given in [2] for the restricted case where the damping coefficient is positive and the spring constant is non-negative are defective. The stability criteria obtained here are expressed in terms of inequalities which impose upper and lower bounds for the system parameters.