Exponential stability analysis and model reduction for spatially interconnected discrete‐time systems with time‐varying delay

This study tackles the problems of exponential stability analysis and model reduction for spatially interconnected discrete‐time systems with time‐varying delay. The well‐posedness, exponential stability, and contractiveness of spatially interconnected discrete‐time systems subject to time‐varying delay are defined and a sufficient condition in terms of linear matrix inequality (LMI) is put forth to test these properties. By exploiting the above analysis result, a sufficient condition for guaranteeing the existence of a reduced‐order system is derived. With the help of Finsler lemma, a reduced‐order system is derived based on the LMI method. By taking advantage of the same method, a delay‐free reduced‐order system for a given spatially interconnected discrete time‐varying delay system can also be attained. Finally, two examples have been carried out to show the feasibility and validity of the derived theories.