Some new rearrangements in sensitivity integrals and concerning inequalities with their application in control

Abstract

In this paper, we extend the sensitivity integrals for linear feedback systems via a non-analytic sensitivity function in Poisson–Jensen’s terminology. First, we sketch a generalized sensitivity integral accounting for the NMP zeros and the RHP poles of the sensitivity function. Interestingly, the sensitivity integral accounting for the NMP zeros becomes a special case of the generalized integral. Then the concerning sensitivity inequality and the associated lower bound are achieved. We also sketch a sensitivity integral that exploits a modified sensitivity function-based approach and stabilizes the linear feedback system. Their concerning sensitivity inequality and the associated lower bound are achieved as well. An illustrative case study example is employed to demonstrate the idea of the ‘sensitivity lower bound’ to choose the ability of controllers for the given linear feedback systems. The rearranged sensitivity lower bound offers simplified analysis involving fewer computation efforts.

Keywords

• Sensitivity functions
• Logarithmic sensitivity integral
• Logarithmic sensitivity inequality
• Loop robustness