SIMO和MISO系统绝对稳定性问题的一个猜想和几个推论

A Conjecture and Its Several Deductions about the Absolute Stability of SIMO and MISO Systems

首先分析了具有多个非线性特性的SIMO和MISO系统的绝对稳定性问题,指出应用已知的频域判据来解决上述问题很难奏效.然后,基于所有孤立部分传递函数都正实的充分必要条件给出了上述系统为稳定的一个猜想,当传递函数的零极点都位于虚轴上时,由这一猜想得到了一个已知的结论;当传递函数的零极点都位于实轴上时,由这一猜想得到了一个新的结论,本文证明该结论是正确的;最后,根据这一猜想,给出了传递函数极点位于复平面的一个例子,它涉及到一类系数矩阵为时变正定矩阵的振动方程的稳定性问题,值得去深入研究.

Firstly, the absolute stability problems of the SIMO and MISO systems with several nonlinear characteristics are analyzed. The difficulty of using the known frequency domain theorems to solve the above problems is presented. Secondly, a conjecture about the stability for these systems is proposed based on the sufficient and necessary condition of the isolated transfer function being positive real. When the zeros and poles of the transfer functions lie in the imaginary axis, a known conclusion is derived from the conjecture; while the zeros and poles are on the real axis, a new result is obtained and is proved in this note. Finally, according to the conjecture, an example with poles existing on the complex plane is presented, which is not only interesting but also challenging.