On the complex stability radius for time-delay differential-algebraic systems

Abstract

An algorithm is proposed for computing the complex stability radius of a linear differential-algebraic system with a single delay and including a neutral term. The exponential factor in the characteristic equation is replaced by its Padé approximant thus reducing the level set method for finding the stability radius to a rational matrix eigenvalue problem. The level set method is coupled with a quadratically convergent iteration. An important condition relating the algebraic constraint and neutral term is introduced to eliminate the presence of characteristic roots approaching the imaginary axis at infinity. The number of iterations of the algorithm is roughly proportional to the numerical value of this condition. Effectiveness of the algorithm is illustrated by numerical examples.