Stability criteria for neutral delay differential-algebraic equations with many delays

Abstract

Abstract In this paper the asymptotic stability is concerned for a class of neutral delay differential-algebraic equations (NDDAEs). We will present two criteria by evaluating a corresponding harmonic function on the boundary of a torus region. Stability regions are also presented so as to locate all possible unstable characteristic roots of NDDAEs. As we know, these roots will make bad numerical simulations. Our criteria help find and avoid them. Numerical examples are shown to check our criteria.

Keywords

• Eigenvalue
• Matrix norm
• Spectral radius
• Asymptotic stability
• Logarithmic norm