AI 中文总结
本文研究正非线性SISO系统的反馈互联，提出PIPO和PITO两个输入输出性质，证明二者结合可保证控制信号有界，还给出了相关结构性条件与实例验证。
AI 中文摘要
本文研究正非线性单输入单输出（SISO）系统的反馈互联，引入两个互补性质：被控对象的持久输入/持久输出（PIPO），以及控制器的持久输入/暂态输出（PITO）。假设闭环系统前向完备，且控制器输出满足单侧仿射增长界，我们证明PIPO与PITO共同蕴含控制信号的有界性。该结果本质上是输入输出层面的，不要求互联子系统具备线性或单调性，但通常无法保证控制器全状态的有界性。我们针对具有$\boldsymbol{\textit{K}}_\boldsymbol{\textit{∞}}$类稳态特性的正单调被控对象，给出了结构性PIPO条件；推导了带显式增益的antithetic integral controller（对偶积分控制器）的PITO性质；并在一个具有乘性控制器增长的非线性积分反馈基序上验证了该框架。
英文摘要
In this paper we study feedback interconnections of positive nonlinear SISO systems and introduce two complementary properties: persistent-input/persistent-output (PIPO) for the plant and persistent-input/transient-output (PITO) for the controller. Assuming forward completeness of the closed loop and a one-sided affine growth bound on the controller output, we show that PIPO and PITO jointly imply boundedness of the control signal. The result is input-output in nature and does not require linearity or monotonicity of the interconnected subsystems, although it does not in general guarantee boundedness of the full controller state. We provide a structural PIPO condition for positive monotone plants with a class-\(\mathcal K_\infty\) steady-state characteristic, establish PITO for the antithetic integral controller with explicit gains, and illustrate the framework on a nonlinear integral-feedback motif with multiplicative controller growth.
