Stability Analysis of Time Delayed System with Coefficient Uncertainty and Time Delay Uncertainty

A general class of linear time invariant (LTI) systems with uncertain coefficient and time delay is studied. This study proposes an approach to determine the joint stability regions of uncertain parameters in both time delay space and coefficient space. The stability boundaries in coefficient-delay space are first obtained by determining stability boundaries in coefficient space. To achieve this, a bilinear transformation is used to transform quasipolynomial into polynomial and the subtle feature of Routh array is exploited. After generating stability boundaries in parametric space, a two-step determination procedure is proposed to extend the paradigm called “cluster treatment of characteristic roots (CTCR)” to the determination of stability regions in coefficient-delay space. A complete example case study is also provided.