On Stability of Discrete-Time Delay-Difference Equations for Arbitrary Delay Variations

This paper focuses on the concept of delay-independent stability for dynamical systems described by continuous-time linear delay-difference equations and the corresponding stability notion in discrete-time domain. The problem will be formulated with respect to delay-parameter space. Our intention is to summarize delay-independent stability condition and to provide, in a compact formulation, an appropriate numerical method for its computation, at least for two dimensional delay case. Obtained results are applied in stability analysis of the discrete-time delay-difference equations. Such a strong stability condition appears to be necessary for the existence of specific invariant regions in the state-space. Some illustrative examples complete the paper.