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.
Highlights
It is well known that time delay, as a natural phenomenon, widely exists in various practical systems such as networked control systems, fuzzy systems and neural networks [1]–[3]
The Lyapunov–Krasovskii functional (LKF) method is a powerful tool to deal with the stability problem for linear delayed systems
A general free-matrix-based (GFMB) summation inequality is developed [40], which leads to a relaxed stability condition for linear discrete-time systems with a time-varying delay
Summary
It is well known that time delay, as a natural phenomenon, widely exists in various practical systems such as networked control systems, fuzzy systems and neural networks [1]–[3]. A general free-matrix-based (GFMB) summation inequality is developed [40], which leads to a relaxed stability condition for linear discrete-time systems with a time-varying delay. Chen: New Results on Stability of Linear Discrete-Time Systems With Time-Varying Delay in [26], in which the quadratic augmented vector contains k −1 k −h1 −1 three vectors x(k), x(i) and x(i), where x(k) is i=k −h1 i=k −h2 the state, h1 and h2 are, respectively, the lower and upper bounds of the discrete-time delay. This proposed LKF is later widely used in the few years in the literature. Sn+ represents the set of symmetric positive-definite matrices of Rn×n
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