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This work carefully revisits the topic of dynamic feedback $ H_{\infty } $ H ∞ control problem for discrete singular systems (DSSs) with time–varying delays. A new state decomposed Lyapunov-Krasovskii functional is presented by a discrete state decomposition method. For the unforced nominal DSSs, delay–dependent sufficient conditions with an $ H_{\infty } $ H ∞ performance index are derived. Based on these conditions, a closed–loop system being regular and causal is developed via a dynamic feedback controller. As a new discrete state decomposition–reorganization method is proposed, the required admissibility conditions are attained. Through the accurate calculation of each decomposition component of the dynamic feedback controller, the desired dynamic feedback controller settings are determined. The numerical findings demonstrate the superiority of our method over earlier approachers, and the results are less conservative. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of delay-dependent stability analysis for systems with interval time-varying delay. By means of a new double free-matrix-based integral inequality and augmented Lyapunov–Krasovskii functionals containing as much information of time-varying delay as possible, a new stability criterion for systems is established. Firstly, by a double integral term two-step estimation approach and combined with single free-matrix-based integral inequalities, a stability criteria is presented. Then, compared with the double integral term two-step estimation approach, the proposed new double free-matrix-based integral inequality with more related time delays has potential to lead to a criterion with less conservatism. Finally, the validity of the presented method is demonstrated by two numerical examples. [ABSTRACT FROM AUTHOR]