Improved Sufficient LMI Conditions for the Robust Stability of Time-delayed Neutral-type Lur’e Systems

New Results on Stability Analysis of Uncertain Neutral‐Type Lur’e Systems Derived from a Modified Lyapunov‐Krasovskii Functional

“…Remark . Recently, [29] improved the stability results of the uncertain neutral-type Lur' e system (1) by combining the extended double integral with Wirtinger-based inequalities technique. In practice, it is known that the range of delay with nonzero lower bound is often encountered, and such systems are referred to as interval time-delay systems.…”

“…So, both the range of delay with zero lower bound and that with nonzero lower bound are considered in this paper. In addition, the lower bound of the delay derivative is also involved in this paper, which is not mentioned in [29].…”

“…Moreover, the paper [22] pointed out that many practical systems can be modeled as neutral time-delayed systems, in which not only the system states or outputs contain time delays, but also the derivative of the system states. Due to the theoretical and practical significance, the analysis of the robust stability of the time-delayed neutral-type Lur' e systems has attached great importance by many scholars [23][24][25][26][27][28][29], where many important robust stability criteria were given. However, the main improvement of stability criteria depends on the development of LKF and the update of inequality techniques based on linear systems.…”

“…However, the main improvement of stability criteria depends on the development of LKF and the update of inequality techniques based on linear systems. For example, recently, [29] improved the stability results of some previous ones by combining the extended double integral with Wirtinger-based inequalities technique; however, the range of delay with nonzero lower bound and 2 Complexity the lower bound of the delay derivative are not involved; in [30], some less conservative stability criteria than some recent previous ones were derived for time-delayed Lur' e system via the second-order Bessel-Legendre inequality approach, a novel inequality technique; in [21], some improved stability criteria for time-delayed neutral-type Lur' e system were given by constructing a novel LKF consisting of a quadratic term and integral terms for the time-varying delays and the nonlinearities, and so on. Recently, C. Zhang [31] considered the effect of the LKFs while discussing the relationship between the tightness of inequalities and the conservatism of criteria for linear systems.…”

Improved robust stability criteria for uncertain linear neutral‐type systems via novel Lyapunov‐Krasovskii functional

“…Therefore, more and more attention is paid to the stability of time-delayed neutral systems. In recent years, the robust stability problem of neutral systems with time delays has been widely studied in [23][24][25][26][27][28][29][30][31][32][33], where many important robust stability criteria are given. However, the main improvement of stability criteria depend on the development of LKF and the update of inequality techniques based on linear systems.…”