Exponential stability of discrete-time linear singular positive time-delay systems

This paper is concerned with the problem of α-exponential stability for discrete-time linear singular positive time-delay systems. Firstly, sufficient and necessary conditions for the positivity of the system are investigated based on the singular value decomposition and monomial coordinate transformation method. Then in virtue of the obtained results, a new exponential stability condition is established. Moreover, all the obtained results are formulated in terms of algebraic matrix inequalities and therefore are numerically tractable. Finally, a numerical simulation is given to show the effectiveness of the proposed techniques.