Stability analysis of discrete-time systems with a time-varying delay via the extended zero-equation method

This brief analyzes the stability of discrete-time systems with a time-varying delay. By adding more state-related vectors and time-varying delay information, an improved Lyapunov-Krasovskii functional is constructed. The extended free-weighting zero-equation method is applied to address the forward difference by combining Finsler’s lemma. As a result, a new and relaxed stability criterion is obtained. Two numerical examples are given to show that the conservatism is greatly reduced.