A Matrix-Separation Approach for Stability of Discrete-Time Systems with Time-Varying Delay
This letter addresses the stability analysis of discrete-time linear systems with time-varying delay using a Lyapunov-Krasovskii functional (LKF) framework. An improved matrix-separation-based inequality (IMSBI) is developed to obtain tighter bounds for the summation terms arising in the forward difference of the LKF. Based on this result, an augmented LKF incorporating additional cross-terms is constructed to capture the interaction between system states and delay evolution. This leads to a less conservative delay-dependent stability criterion expressed as linear matrix inequalities (LMIs). Numerical results demonstrate improved stability margins and a reduced number of decision variables compared with existing methods.
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