Discrete-Delay-Independent and Discrete-Delay-Dependent Criteria for a Class of Neutral Systems

Abstract

In this paper, the asymptotic stability for a class of neutral systems with discrete and distributed multiple time delays is considered. Discrete-delay-independent and discrete-delay-dependent criteria are proposed to guarantee stability for such systems. The resulting stability criteria are written in the form of spectral radius and linear matrix inequality (LMI). Some numerical examples are given to illustrate that our obtained results are less conservative.

On delay‐dependent LMI‐based guaranteed cost control of uncertain neutral systems with discrete and distributed time‐varying delays

“…By Schur complement of [26], the condition C 1 50 in (5a) is equivalent to C 0 50 in (8). By the Schur complement of [26] with C 0 50; we have c 3 50 in (7e).…”

“…By increasing the number of summands and simultaneously decreasing the differences between neighbouring argument values, one naturally arrives at equations with distributed (or continuous) and mixed (both distributed and discrete) delay arguments. In view of [5,8], the distributed delays play an important role in the stability of system. Depending on whether the stabilizability criterion itself contains the size of delays, criteria of such systems can be classified into two categories, namely delay-independent criteria [5,8] and delay-dependent criteria [5,8].…”

“…In view of [5,8], the distributed delays play an important role in the stability of system. Depending on whether the stabilizability criterion itself contains the size of delays, criteria of such systems can be classified into two categories, namely delay-independent criteria [5,8] and delay-dependent criteria [5,8]. Generally speaking, the latter ones are less conservative than the former ones, but the former ones are also useful when the effect of time delay is small.…”

Further results on delay-dependent robust stability conditions of uncertain neutral systems

“…This neutral system was considered in References [10,11,12,16,20,21]. The results on the maximum allowed % h h are compared in Table I (figures are as reported in corresponding papers).…”

Stability of Internet-Based Control Systems with Uncertainties and Multiple Time-Varying Delays

“…This motivates the present stability investigation of multi-rate Internet-based control systems with time-varying delay and uncertainties. We found that such multi-rate Internet-based control systems can be rewritten as a time-delay system through our modeling process, and there are many results in the fields [4], [8], [9], [17], [25], [27].These criteria can be classified into two categories according to their dependence on the size of the delays, namely, delay-independent stability criteria [18], [19], [20], and delay-dependent stability criteria [21], [22], [23], [24]. The delay-independent stability criteria guarantee the stability of the system irrespective of the size of the time-delay.…”