New mixed‐delay‐dependent robust stability conditions for uncertain linear neutral systems

Abstract

In this study, mixed-delay-dependent robust stability problem is investigated for uncertain linear neutral systems with mixed delays. The existing stability conditions are obtained by employing the information of neutral delay and discrete delay independently, and are conservative to some extent. Different from most existing methods, this study attempts to introduce the interconnected information between neutral delay and discrete delay. Based on such an idea, the simple stability and robust stability conditions are firstly proposed by integral inequality method, then improved stability and robust stability conditions are obtained by incorporating delay-decomposition idea and augmented Lyapunov-Krasovskii functional. Theory analysis and examples show the benefits of the proposed techniques and conditions.

Improved conditions for neutral delay systems with novel inequalities

“…With different cases, we can obtain different maximum time delay h by using Matlab toolbox as listed in Table 1, compared with some existing references. From Table 1, we can see that the results in [2] and [1] are close to our results. However, the maximum of h using Theorem 3.1 is nearly close to analytical bounds, which shows our approach is less conservative than the existing results.…”

“…Various interesting methods have been introduced to obtain delay-dependent stability conditions for neutral delay systems, such as model transformation approach [8], delay partitioning technique [2], discretized Lyapunov functional method [11], free-weighting matrix approach [9,12], and integral inequality method [1]. With the help of these approaches, improved delay-dependent stability conditions have been presented gradually, such as [3,11,15] and the references therein.…”

Steroid-photosensitizer conjugates: Syntheses and applications

“…In this section, we review the various synthetic approaches to prepare such conjugates, and where available, biological data are also summarized. The synthesis of a series of E 2 -porphyrin conjugates 1 in which porphyrin moieties are attached via the 3-hydroxyl of E 2 was reported by Chen et al [26]. However, substitution of the 3-hydroxyl group of E 2 leads to loss of ER-binding affinity.…”

Improved robust stability conditions for uncertain neutral systems with discrete and distributed delays

“…Based on such an idea, we recently proposed the improved mixed-delay-dependent stability conditions in [33] for linear neutral systems by incorporating the relationship between discrete delay and neutral delay sufficiently. In this paper, the main objective is to obtain the less conservative stability and robust stability conditions for uncertain neutral systems with discrete and distributed delays.…”

“…In this paper, the main objective is to obtain the less conservative stability and robust stability conditions for uncertain neutral systems with discrete and distributed delays. Similar to the ideas in [32][33], we attempt to incorporate the relationships between discrete delay, neutral delay and distributed delay to reduce the conservatism. However, different from the techniques in [32][33], where the relationships between two discrete delays, and discrete and neutral delays are reflected by the terms x(t −h) and x(t −τ), this paper attempts to reflect the relationship between discrete (neutral) delay and distributed delay precisely by the terms x(t − h)(x(t − τ)) and t t−r x(s) ds.…”