New Results on Stability of Linear Discrete-Time Systems With Time-Varying Delay

Abstract

This paper is concerned with the stability problem for linear discrete-time systems with a time-varying delay. Some relations between two general free-matrix-based summation inequalities are discussed. A novel Lyapunov-Krasovskii functional (LKF) is proposed by modifying the single-and double-summation LKF terms. As a result, a new stability condition is obtained by employing the general free-matrix-based summation inequalities reported recently. Numerical examples are given to show that the obtained stability condition is more relaxed than some of existing results. INDEX TERMS Discrete-time system, free-matrix-based inequality, Lyapunov functional, stability, timevarying delay.

An Improved Stability Criterion for Discrete-Time Linear Systems With Two Additive Time-Varying Delays

“…If the double summation terms and ∆x(k) are removed from V 1 (k), V 3 (k) and V 5 (k), respectively. the LKFs ( 11), ( 45) and (52) in this paper reduce to those in the literature [39], [46]. To highlight the advantages of the augmented LKFs, the corresponding LKFs by removing the augmented terms are given in the following forms.…”