Positivity and stability analysis for linear implicit difference delay equations

This paper deals with positivity and stability of linear implicit difference delay equations. Being different from the Lyapunov function approach commonly used in stability analysis, the method employed in this paper gives a way to solve the exponential stability of linear implicit difference equations with time-varying delay. By decomposition state-space and mathematical induction method, new necessary and sufficient conditions for positivity and stability of such systems are derived. Numerical examples are given to illustrate the proposed results.