Stability feeler: a tool for parametric robust stability analysis and its applications

In this study the authors propose a new tool for robust stability analysis. This tool gives D-stability intervals along a given line in the polynomial coefficient space. D-stability means that all the zeros of characteristic polynomials are in a prescribed connected open region and therefore, besides continuous-time systems or discrete-time systems, any systems having such a pole location can be analysed by utilising this tool. The tool is referred to as ´stability feeler´, named after a feeler of insects. It is shown that stability feeler can be systematically computed by using standard numerical calculations. The authors also show two applications of stability feeler. One is the design of robust controllers for linear uncertain systems. The other is robust absolute stability analysis of Lur´e systems. For the robust controller design, it is often necessary to analyse stability of systems with the designed controllers. However, by the support of stability feeler, the authors can directly obtain a class of stabilising controllers. For robust absolute stability of interval Lur´e systems, a sufficient condition has already been proposed, while stability feeler enables one to analyse stability of both continuous-time and discrete-time Lur´e systems with affine linear uncertainties, which are more general than interval ones. Moreover, sharpness of any robust absolute stability criteria for uncertain Lur´e systems can be assessed.