On the Stability Analysis of Delay Differential-Algebraic Equations

Abstract

The stability analysis of linear time invariant delay differential- algebraic equations (DDAEs) is analyzed. Examples are delivered to demonstrate that the eigenvalue-based approach to analyze the exponential stability of dynamical systems is not valid for an arbitrarily high index system, and hence, a new concept of weak exponential stability (w.e.s) is proposed. Then, we characterize the w.e.s in term of a spectral condition for some special classes of DDAEs.

Keywords: Differential-algebraic equation, time delay, exponential stability, weak stability, simultaneous triangularizable.

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Mathematics Subject Classification (2010): 34A09, 34A12, 65L05, 65H10.