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This paper further studies the stability of the uncertain delayed neutral-type system by constructing a novel Lyapunov-Krasovskii functional (LKF) with some delay-dependent and N-dependent items. Some new delay-dependent robust stability criteria are proposed based on linear matrix inequality (LMI). The criteria proposed in this paper are less conservative than some recent previous ones. Some numerical examples, including a linear neutral-type system, the partial element equivalent circuit and a general linear system, are presented to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of delay-dependent robust $$H_\infty $$ control for uncertain systems with time-varying delays and norm-bounded parameter uncertainties. Firstly, some new delay-dependent stability criteria are proposed by exploiting a new Lyapunov-Krasovskii functional and free-weighting matrices method. Secondly, based on the criteria obtained, a delay-dependent criterion for the existence of a memoryless state feedback $$H_\infty $$ controller that ensures asymptotic stability and a prescribed $$H_\infty $$ performance level of the closed-loop system for all admissible uncertainties is proposed in terms of linear matrix inequalities (LMIs). These developed results enjoy much less conservatism than the existing ones due to the introduction of delay segmentation approach to estimate the upper bound of the derivative of Lyapunov functional without ignoring some useful terms that take into account information of the time-delay. Finally, numerical examples are provided to demonstrate the effectiveness and benefits of the proposed method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the delay-dependent synchronization criterion for stochastic complex networks with time delays. Firstly, expectations of stochastic cross terms containing the Itô integral are investigated by utilizing stochastic analysis techniques. In fact, in order to obtain less conservative delay-dependent conditions for stochastic delay systems including stochastic complex (or neural) networks with time delays, how to deal with expectations of these stochastic cross terms is an important problem, and expectations of these stochastic terms were not dealt with properly in many existing results. Then, based on the investigation of expectations of stochastic cross terms, this paper proposes a novel delay-dependent synchronization criterion for stochastic delayed complex networks. In the derivation process, the mathematical development avoids bounding stochastic cross terms. Thus, the method leads to a simple criterion and shows less conservatism. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The global exponential stability for a class of uncertain delayed neural networks (DNNs) of neutral type with mixed delays is investigated in this paper. Delay-dependent and delay-independent stability criteria are proposed to guarantee the robust stability and uniqueness of equilibrium point of DNNs via linear matrix inequality and Razumikhin-like approaches. Two classes of perturbations on weighting matrices are considered in this paper. Some numerical examples are illustrated to show the effectiveness of our results. [ABSTRACT FROM AUTHOR]

This paper addresses the mean square consensus problem of leader‐following stochastic multi‐agent systems using a distributed event‐triggered control strategy. For each involving agent, generally, the time‐varying (or fixed) delay between controller and actuator is unavoidable. The controller is updated only when the event condition is triggered. Based on the Lyapunov function method and Itô formula, three sufficient conditions for leader‐following mean square consensus are established, including a delay‐independent consensus condition and a delay‐dependent criterion for the case with input fixed time delay, and a consensus criterion for the case with input time‐varying delay. Furthermore, an inter‐event time lower bound between two sampling points is derived. The results are illustrated through several numerical examples. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of passivity-based control for Markovian jump systems via retarded output feedback controllers. A delay-dependent passivity criterion is obtained in terms of linear matrix inequalities. Based on this, a sufficient condition is proposed for the design of a retarded output feedback controller which ensures that the closed-loop system is passive. By using the sequential linear programming matrix method, a desired retarded output feedback controller can be constructed. Numerical examples are provided to demonstrate the advantage and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents a predictive synchronization method for discrete-time chaotic Lur'e systems with input constraints by using time-varying delayed feedback control. Based on the model predictive control scheme, a delay-dependent stabilization criterion is derived for the synchronization of chaotic systems that is represented by Lur'e systems with input constraints. By constructing a suitable Lyapunov-Krasovskii functional and combining with a reciprocally convex combination technique, a delay-dependent stabilization condition for synchronization is obtained via linear matrix inequality (LMI) formulation. The control inputs are obtained by solving a min-max problem subject to cost monotonicity, which is expressed in terms of LMIs. The effectiveness of the proposed method will be verified throughout a numerical example. [ABSTRACT FROM AUTHOR]

Abstract: The switching signal (switching law) design for robust global exponential stability of switched nonlinear systems is investigated in this paper. LMI-based delay-dependent criteria are proposed to design the switching signal and guarantee the global exponential stability. Free weighting matrix and additional nonnegative inequality approaches are used in this paper to find the less conservative stability results. Finally, some numerical examples are illustrated to show the main improvement. [ABSTRACT FROM AUTHOR]

A robust reliable control with integral quadratic constraint (IQC) performance for a class of uncertain systems with state and input delays is considered in this paper. Two classes of failure situations for sensor or actuator are studied. In the first class, a delay-dependent criterion for time-delay systems without perturbations is proposed to design the reliable control with IQC performance. Next, a criterion for uncertain time-delay systems with parameter uncertainties is obtained via simple derivations. The linear matrix inequality (LMI) approach is used to design a robust reliable state feedback control with IQC performance. In the second class, a reliable control with IQC performance is also provided from he previous method. A numerical example is given to illustrate the effectiveness of the procedure. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the problem of exponential stability in mean square for stochastic systems with multiple delays is investigated. A delay-dependent sufficient condition is derived in terms of linear matrix inequalities (LMIs) by using a descriptor model transformation of the system and by applying Moon''s inequality for bounding cross terms. The criteria obtained in this paper can be tested numerically very efficiently using interior point algorithms. An example shows that the proposed methods are less conservative than the other methods. [Copyright &y& Elsevier]

This paper considers the guaranteed cost control problem for a class of uncertain linear systems with both state and input delays. By representing the time-delay system in the descriptor system form and using a recent result on bounding of cross products of vectors, we obtain new delay-dependent sufficient conditions for the existence of the guaranteed cost controller in terms of linear matrix inequalities. Two examples are presented which show the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

The article presents absolute stability analysis for time-delay Lur'e systems with both sector- and slope-restricted nonlinearities. Topics include a new delay-dependent stability criterion given by using a Lur'e-Postnikov functional, the additional slope restrictions on the nonlinearities stated to play important roles in improving the absolute stability conditions and development of control theory impelling many advanced control techniques, such as neural network and sliding mode control.

Abstract: This paper discusses the mean-square exponential stability of stochastic linear systems of neutral type. Applying the Lyapunov–Krasovskii theory, a linear matrix inequality-based delay-dependent stability condition is presented. The use of model transformations, cross-term bounding techniques or additional matrix variables is all avoided, thus the method leads to a simple criterion and shows less conservatism. The new result is derived based on the generalized Finsler lemma (GFL). GFL reduces to the standard Finsler lemma in the absence of stochastic perturbations, and it can be used in the analysis and synthesis of stochastic delay systems. Moreover, GFL is also employed to obtain stability criteria for a class of stochastic neutral systems which have different discrete and neutral delays. Numerical examples including a comparison with some recent results in the literature are provided to show the effectiveness of the new results. [Copyright &y& Elsevier]

The robust H∞ control problem is considered for a class of uncertain neutral system involving both state and control input time-varying delays. The uncertainties under consideration are nonlinear time-varying parameter perturbations. The methodology is based on the Lyapunov functional combined with a unified LMI approach, and a new delay-dependent criterion is proposed to guarantee the stabilization and disturbance attenuation of systems. Moreover, a convex optimization approach is used to solve the robust H∞ control disturbance attenuation problem. Finally, a numerical example is illustrated to show the validity of this paper. The simulation results reveal significant improvement over the recent results. [ABSTRACT FROM AUTHOR]

In this brief, free-weighting matrices are employed to express the relationship between the terms in the Leibniz-Newton formula; and based on that relationship, a new delay-dependent exponential-stability criterion is derived for delayed neural networks with a time-varying delay. Two numerical examples demonstrate the improvement this method provides over existing ones. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with delay Lur''e control systems with multiple nonlinearities and time-varying structured uncertainties. First, some sufficient, and necessary and sufficient conditions for the existence of a Lyapunov functional in the extended Lur''e form with a negative definite derivative that guarantees delay-independent robust absolute stability are presented. Then, some new less conservative delay-dependent absolute stability criteria are derived that employ free weighting matrices to express the relationships between the terms in the Leibniz–Newton formula. All the criteria are based on linear matrix inequalities. Finally, a numerical example is presented to illustrate the effectiveness of the method. [Copyright &y& Elsevier]

The problem of sliding‐mode control (SMC) with dissipativity for a class of time‐delay Takagi–Sugeno fuzzy singular systems is investigated. The system is subject to uncertainties and input non‐linearity. Based on an integral sliding surface, a delay‐dependent criterion is developed in terms of linear matrix inequalities, which ensures the sliding mode dynamics to be robustly admissible and strictly (𝓆𝒮ℛ)‐dissipative. Moreover, an SMC law is established such that the reachability of the specified sliding surface is guaranteed. Finally, the validity and applicability of the proposed approach are illuminated by two simulation examples. [ABSTRACT FROM AUTHOR]

This note deals with the problem of stabilization/stability for neutral systems with nonlinear perturbations. A new stabilization/stability scheme is presented. Using improved Lyapunov functionals, less conservative stabilization/ stability conditions are derived for such systems based on linear matrix inequalities (LMI). Numerical examples are provided to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature. [ABSTRACT FROM AUTHOR]

The nonfragile H∞ control problem for a neutral system with time-varying delays is considered. Delay-dependent criteria are proposed to guarantee the stabilization and disturbance attenuation of systems. A linear matrix inequality optimization approach is used to solve the nonfragile H∞ control problem. Nonfragile H∞ control for an unperturbed neutral system is investigated first. Then, nonfragile H∞ control for an uncertain neutral system is derived directly from the unperturbed case. Finally, two examples are illustrated to show the improvement of this correspondence. [ABSTRACT FROM AUTHOR]

The design of a robust mixed H2/H∞ controller for a class of uncertain neutral systems with discrete, distributed, and input time-varying delays is considered. More precisely, the proposed robust mixed H2/H∞ controller minimizes an upper bound of the H2 performance measure, while guaranteeing an H∞ norm bound constraint. Based on the Lyapunov-Krasovskii functional theory, a delay-dependent criterion is derived for the existence of a desired mixed H2/H∞ controller, which can be constructed easily via feasible linear matrix inequalities (LMIs). Furthermore, a convex optimization problem satisfying some LMI constraints is formulated to obtain a suboptimal robust mixed H2/H∞ controller achieving the minimization of an upper bound of the closed-loop H2 performance measure. Finally, a numerical example is illustrated to show the usefulness of the obtained design method. [ABSTRACT FROM AUTHOR]

A master-slave synchronization scheme for Lur'e systems is studied for a known delay existing between master and slave systems. Based on the latest development of stability studies for time-delay systems, a new delay-dependent synchronization criterion is derived by the free-weighting matrix approach. The criterion shown by example is less conservative than the existing synchronization criteria. [ABSTRACT FROM AUTHOR]

This article concerns a coupled LMIs approach to delay-dependent observer-based output feedback stabilizing controller design for linear continuous-time systems with multiple state delays. The advantage of our proposed delay-dependent coupled LMIs criterion lies in that: ( 1 ) it can optimize one of multiple time delays with others selected properly, and at the same time, the feedback-gain and observer-gain can be obtained, respectively. (2) it is less conservative than the existing delay-independent ones in the literature. Algorithm to solve the coupled LMIs is also given. Numerical examples illustrate the effectiveness of our method. [ABSTRACT FROM AUTHOR]