Stability Results of Popov‐Type for Infinite‐Dimensional Systems with Applications to Integral Control
Stability Results of Popov‐Type for Infinite‐Dimensional Systems with Applications to Integral Control
复制标题
无限维系统波波夫型稳定性结果及其在积分控制中的应用
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发表时间：
2003
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通讯作者：
O. Staffans
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作者：
R. Curtain;H. Logemann;O. Staffans
我们得到了无限维系统在输入输出条件下的绝对稳定性的波波夫型结果。我们的结果适用于反馈系统，其中线性部分是L2稳定线性系统和积分器的串联互连，并且非线性满足扇形条件，该条件允许低增益等于零的非线性（例如饱和，或者更一般地说，有界非线性）。这些结果用于证明低增益积分反馈控制的收敛性和稳定性，该控制适用于受致动器和传感器非线性影响的L2稳定线性系统。所考虑的执行器/传感器非线性类包含在控制工程中很重要的标准非线性，如饱和和死区。此外，我们利用所开发的输入-输出理论，推导出强稳定良定无限维线性系统的绝对稳定性和低增益积分控制的状态空间结果。2000数学学科分类45M05、45M10、93B52、93C10、93C20、93C25、93D05、93D09、93D10、93D25。
We derive absolute stability results of Popov‐type for infinite‐dimensional systems in an input‐output setting. Our results apply to feedback systems where the linear part is the series interconnection of an L2‐stable linear system and an integrator, and the non‐linearity satisfies a sector condition which allows for non‐linearities with lower gain equal to zero (such as saturation, or more generally, bounded non‐linearities). These results are used to prove convergence and stability properties of low‐gain integral feedback control applied to L2‐stable linear systems subject to actuator and sensor non‐linearities. The class of actuator/sensor non‐linearities under consideration contains standard non‐linearities which are important in control engineering such as saturation and deadzone. Moreover, we use the input‐output theory developed to derive state‐space results on absolute stability and low‐gain integral control for strongly stable well‐posed infinite‐dimensional linear systems. 2000 Mathematics Subject Classification 45M05, 45M10, 93B52, 93C10, 93C20, 93C25, 93D05, 93D09, 93D10, 93D25.