Fragility analysis for control systems
控制系统的脆弱性分析

Fragility means that the stability of a closed-loop system is extremely sensitive to parameter perturbations. For these systems, the open-loop frequency response is closely passing by the critical stability point (-1; j0), and the fragile relationship with the point (-1; j0) can easily be violated by any possible perturbation. It is analyzed and pointed out that the fragility of a control system can be quantitatively analyzed by using the Bode integrals. For non-minimumphase unstable plants, the unstable pole of the controller in addition with the unstable pole of the plant may greatly increase the peak of the sensitivity function. So the resulting design for such systems is unavoidably fragile. For multivariable unstable plants, there may be a rather large unstable pole in an equivalent output feedback loop, which can also cause a large peak of the sensitivity function and results in a fragile design. The Bode integral can also be used to avoid the fragility of the design.