A simplified robust circle criterion using the sensitivity-based quantitative feedback theory formulation

The circle criterion provides a sufficient condition for global asymptotic stability for a specific class of nonlinear systems, those consisting of th e feedback interconnection of a single-input single-output linens dynamic s ystem and a static, sector-bounded nonlinearity. Previous authors (Wang et al., 1990) have noted the similarity between the graphical circle criterion and design bounds in the complex plane stemming from the Quantitative Feed back Theory (QFT) design methodology. The QFT formulation has specific adva ntages from the standpoint of controller synthesis. However, the aforementi oned approach requires that plant uncertainty sets (i.e., "templates") be m anipulated in the complex plane. Recently, a modified formulation for the Q FT linear robust performance and robust stability problem has been put forw ard in terms of sensitivity function bounds. This formulation admits a para metric inequality which is quadratic in the open loop transfer function mag nitude, resulting in a computational simplification over the template-based approach. In addition, the methodology admits mired parametric and nonpara metric plant models. The disk inequality which results represents a much cl oser analog of the circle criterion requiring only scaling and a real axis shift This observation is developed in this paper, and the methodology is d emonstrated in this paper via feedback design and parametric analysis of a quarter-car active suspension model with a sector nonlinearity.