An improved stability criteria for neutral-type Lur’e systems with time-varying delays

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

“…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.…”

“…As is known to all, Lur' e system, which is composed of the feedback connection of the linear dynamical system and the nonlinearity satisfying the sector-bounded condition, can represent many deterministic nonlinear systems, for example, Chua's Circuit and the Lorenz system [17]. Therefore, the study on the stability of Lur ' e systems becomes more and more popular [18][19][20][21]. 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.…”

“…Inspired by the above analysis, the following ideas of reducing the conservation of the previous proposed stability criteria should be addressed: (i) A modified LKF with the above both classes of Lyapunov matrices, that is delay-product-type and delay-dependent matrices, is constructed. Compared with the general LKFs in some previous published papers, such as [21,28,30], the Lyapunov matrices of the nonintegral item are just symmetrical, not always positive definite, which can extend the freedom for checking the feasibility of stable conditions based on LMI. And the delay-dependent matrices of the singleintegral items are utilized, which can also further improve the utilization of time delay and its derivative information.…”

New absolute stability results for Lurie systems with interval time‐varying delay based on improved Wirtinger‐type integral inequality

“…On the other hand, the time delay, as one of primary sources to instability and poor performance, is invariably encountered in various dynamic systems such as engineering system, biological system, chemical system, and electrical networks. The absolute stability for Lurie system with time delay thus attained considerable significance during the past decades . Generally speaking, so far, the obtained absolute stability criteria for the delayed Lurie system can be categorized as two types, ie, the delay‐independent ones and the delay‐dependent ones.…”

“…The absolute stability for Lurie system with time delay thus attained considerable significance during the past decades. [7][8][9][10][11][12][13][14][15][16][17][18][19] Generally speaking, so far, the obtained absolute stability criteria for the delayed Lurie system can be categorized as two types, ie, the delay-independent ones and the delay-dependent ones. Due to sufficiently considering the information of 2422…”