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A state tracking control problem for a class of semi-Markovian jump systems (SMJSs) with input delay and disturbances is addressed in this study. In particular, an improved-equivalent-input-disturbance estimator approach (IEIDEA)-based truncated predictive controller is designed to synchronously compensate the effect of unknown external disturbances and time-varying delay. Specifically, by making use of IEIDEA, the unknown disturbances are estimated with high precision and incorporated into the control input channel, which eases the way to achieve the desired tracking performances. Specifically, the state predictor satisfies the delay-free state-space equation and is used in controller design along with prediction. In accordance with linear matrix inequality framework and Lyapunov stability theory, a set of adequate conditions are established to guarantee the state tracking performance of SMJSs. Finally, the numerical examples with simulation results are provided to validate the efficacy and practicability of the established control technique. • An improved-equivalent-input-disturbance estimator approach (IEIDEA)-based truncated predictive controller is designed. • IEIDE is incorporated for the state prediction accuracy. • To address the input delay effect, a novel predictive feedback control strategy is devised. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies the problem of state estimation for static neural networks with time-varying delay. By construction of a suitable Lyapunov–Krasovskii functional, some improved delay-dependent conditions are established such that the error system is globally exponentially stable with a decay rate and a prescribed performance is guaranteed. In order to get less conservative results of the state estimation condition, zero equalities and reciprocally convex approach are employed. The estimator gain matrix can be obtained in terms of the solution to linear matrix inequalities. Numerical examples are provided to illustrate the effectiveness and performance of the developed method. [Copyright &y& Elsevier]

Abstract: This paper concerns the problem of delay-dependent stability criteria for neural networks with interval time-varying delays. First, by constructing a newly augmented Lyapunov–Krasovskii functional and combining with a reciprocally convex combination technique, less conservative stability criterion is established in terms of linear matrix inequalities (LMIs), which will be introduced in . Second, by taking different interval of integral terms of Lyapunov–Krasovskii functional utilized in , further improved stability criterion is proposed in . Third, a novel approach which divides the bounding of activation function into two subinterval are proposed in to reduce the conservatism of stability criterion. Finally, through two well-known numerical examples used in other literature, it will be shown the proposed stability criteria achieves the improvements over the existing ones and the effectiveness of the proposed idea. [Copyright &y& Elsevier]

Abstract: In this paper, a nonlinear model predictive control method is presented for solid oxide fuel cell systems. For realistic modeling, a sector bounded nonlinear model with input constraint is considered. As a performance index, we consider one horizon cost function that is represented by the weighted sum of state, control input and nonlinear function. By minimizing the upper bound of the cost function, the optimized control input sequences are obtained. For cost monotonicity, a terminal inequality condition is derived in terms of a finite number of linear matrix inequalities (LMIs) by using augmented vector feedback law which consists of state and sector bounded nonlinear function. In order to show the effectiveness of the proposed method, the sector bounded nonlinear model is derived for the solid oxide fuel cell systems and the system performance is verified by applying the proposed MPC algorithm to the systems. [Copyright &y& Elsevier]

Abstract: This paper presents a method for gain analysis of discrete-time systems with saturation nonlinearity by using an augmented Lyapunov functional. By using sector and slope properties of the saturation nonlinearity, the gain performance criterion is obtained via LMI formulation. The proposed Lyapunov function have augmented quadratic form with states as well as the sector bounded nonlinear function. Numerical examples show that the proposed method is less conservative than the existing ones. [Copyright &y& Elsevier]

Abstract: In this paper, a robust filtering problem is considered for a class of discrete-time nonlinear systems. Based on the Lyapunov method, a design criterion of the robust filter guarantee not only the stability but also the prespecified upper bound of norm from the disturbance inputs to error state outputs. The design condition can be solved easily by efficient convex optimization algorithms. Numerical examples show the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper deals with the absolute stability analysis for uncertain time delay Lur’e systems that have time-varying delays and sector and slope restricted nonlinearities. New delay-dependent stability criteria are derived via linear matrix inequality (LMI) formulation that can be easily solved by various optimization techniques. Sector bounds and slope bounds are employed to the Lyapunov–Krasovskii functional through convex representation of the nonlinearities so that less conservative stability conditions are obtained. Numerical examples show effectiveness of the proposed stability condition. [Copyright &y& Elsevier]

Abstract: In this paper, we present a novel method for the robust control problem of uncertain nonlinear discrete-time linear systems with sector and slope restrictions. The nonlinear function considered in this paper is expressed as convex combinations of sector and slope bounds. Then the equality constraint is derived by using convex properties of the nonlinear function. A stabilization criterion for the existence of the state feedback controller is derived in terms of linear matrix inequalities (LMIs) by using Finsler’s lemma. The proposed method is demonstrated by a system with saturation nonlinearity. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a robust dynamic output feedback model predictive controller (MPC) design for linear parameter varying (LPV) systems. According to the proposed MPC algorithm, the control law is computed based on linear matrix inequality (LMI) at each sampling time by solving convex optimization problem. Also, a new parameter-dependent Lyapunov function is proposed to get a less conservative condition for stability of the system. The effectiveness of the result proposed is verified via a numerical example. [Copyright &y& Elsevier]

This paper investigates the stability criteria of time-varying delay systems with known bounds of the delay and its derivative. To obtain a tighter bound of integral term, quadratic generalized free-weighting matrix inequality (QGFMI) is proposed. Furthermore, a novel augmented Lyapunov–Krasovskii functional (LKF) are constructed with a delay-dependent matrix, which impose the information for a bound of delay derivative. Relaxed stability condition using QGFMI and LKF provides a larger delay bound with low computational burden. The superiority of the proposed stability condition is verified by comparing to recent results. [ABSTRACT FROM AUTHOR]

• This paper investigates affine transformed sampled-data control problems for fuzzy semi-Markov jump systems (FSMJSs). • To solve parameterized LMI (PLMI), a novel convex relaxation technique is proposed for a less conservative stabilization criteria of FSMJSs. • New mismatched PLMI with the proposed controller provides a larger region of the feasible solution compared to the non-affine membership function. This article investigates affine transformed sampled-data control problems for fuzzy semi-Markov jump systems (FSMJSs). First of all, in the novel fuzzy sampled-data control, an affine transformed membership function is introduced, which contributes to constructing the synchronous time scale grades of membership without any constraint condition. Then, by utilizing a mode-dependent Lyapunov function with the looped functions, a sufficient condition concerning the asymptotical stability of the closed-loop FSMJSs is established in the form of linear matrix inequality (LMI). Meanwhile, to solve parameterized LMI (PLMI), a novel convex relaxation technique is proposed, based on which less conservatism stabilization criteria of FSMJSs, and a maximum sampling interval with respect to sampled-data control are further derived. Finally, two examples are carried out to manifest numerically the validity of the raised method. [ABSTRACT FROM AUTHOR]

• By adopting T-S fuzzy model concept, the tracking control design problem of NSMJSs with disturbances and uncertainties is investigated. • An estimated lumped disturbance is incorporated into the fuzzy rule based mode-dependent control design so as to deal with the effect of disturbances and uncertainties. • The sufficient conditions in the structure of LMIs are derived to determine the desired modedependent controller gain matrices. • At last, the single-link robot arm model is adopted to validate the usefulness, practicability and inherent potential of the developed control protocol. The focus of this paper is on solving the state tracking control problem for a class of fuzzy semi-Markovian jump systems with the aid of fuzzy modeling approach. Besides, the impact of both unexpected disturbances and uncertainties in fuzzy semi-Markovian jump systems is considered. In particular, the nonlinearity in the addressed system is represented by the T-S fuzzy model, wherein the disturbances and uncertainties are estimated by precisely considering uncertainty and disturbance estimator (UDE)-based control approach. Whilst, the desired fuzzy rule-based mode-dependent control law is formulated by exploiting the parallel distributed compensation strategy and estimated output of disturbances and uncertainties. In the proposed tracking control scheme, the resilient strategy is considered to overcome the impact of gain perturbations. Further, in terms of LMIs, a set of sufficient constraints is derived in accordance with the appropriate selection of mode-dependent fuzzy rule-based Lyapunov function. Under which, the asymptotic tracking and enhanced disturbance rejection performances are guaranteed for the system under consideration. Notably, the desired control gain matrices are determined by solving the derived sufficient conditions via MATLAB LMI toolbox. Conclusively, a single-link robot arm model is adopted to justify the practicability and efficacy of the theoretical findings. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the problem of exponential passivity analysis for uncertain neural networks with time-varying delays is considered. By constructing new augmented Lyapunov–Krasovskii’s functionals and some novel analysis techniques, improved delay-dependent criteria for checking the exponential passivity of the neural networks are established. The proposed criteria are represented in terms of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms. A numerical example is included to show the superiority of our results. [Copyright &y& Elsevier]

Abstract: In this paper, the problem of delay-dependent stability for uncertain neutral systems with time-varying delays is considered. The parameter uncertainties are assumed to be norm-bounded. By constructing an augmented Lyapunov functionals, a novel delay-dependent stability criterion for the system is established in terms of LMIs (linear matrix inequalities). Six numerical examples are given to show the effectiveness of proposed method. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a new delay-dependent stability criterion for dynamic systems with time-varying delays and nonlinear perturbations. Based on the Lyapunov method, a sufficient delay-dependent criterion for asymptotic stability is derived in terms of linear matrix inequality (LMI). Numerical examples are given to show the effectiveness of our result. [Copyright &y& Elsevier]

Abstract: In this paper, the problem of a new delay-dependent robust stability criterion for neutral systems is investigated. The considered system has time-varying structured uncertainties and interval time-varying delays. Based on the Lyapunov method, a delay-dependent criterion for asymptotic stability is established in terms of LMI (linear matrix inequality). Numerical examples are carried out to support the effectiveness of our results. [Copyright &y& Elsevier]

Abstract: In this paper, the design problem of state estimator for a class of neural networks of neutral-type with interval time-varying delays is studied. The interval time-varying delay does not have constraint that its derivative is less than 1. The constraint is widely used to deal with time-varying delays in many papers. A delay-dependent linear matrix inequality (LMI) criterion for existence of the estimator is proposed by using Lyapunov method. The criterion can be easily solved by various convex optimization algorithms. A numerical example is given to show the effectiveness of proposed method. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a new stability criterion for uncertain neutral systems. The considered system has time-varying structured uncertainties and time-varying delay. Based on the Lyapunov method, a delay-dependent criterion for asymptotic stability is derived in terms of LMI (linear matrix inequality). Numerical examples are given to show the effectiveness of our results. [Copyright &y& Elsevier]

Abstract: In this paper, the global asymptotic stability of delayed cellular neural networks of neutral-type is investigated. A novel delay-dependent criterion for the stability using the Lyapunov stability theory and linear matrix inequality (LMI) framework is presented. Since the condition is dependent on the size of time delay, it is usually less conservative than delay-independent ones. Two numerical examples are given to show the effectiveness of proposed method. [Copyright &y& Elsevier]

Abstract: In this paper, a design method for a new controller to control the Genesio–Tesi chaotic systems is proposed. In this work, a dynamic outputs feedback controller for the system is developed for the first time. For stability analysis, a well-known Lyapunov stability theorem combining with LMI (linear matrix inequality) optimization approach is utilized. A numerical simulation is presented to show the usefulness of the proposed control scheme. [Copyright &y& Elsevier]

• Proportional-plus-integral (PI) event-triggered scheme is employed to reduce average usage of samples. • Affinely transformed membership based distributed filter (AMDF) is utilized to enhance H ∞ performance. • Deviation bounds between original membership function and affine matched one are considered in consecutive sampling time. This paper handles a design of event-triggered H ∞ filter for T-S fuzzy systems in the connection of network communication. The sampled-data fuzzy filter, which take into account both the measurement output and the fuzzy consequent parameter as the sampled signal, is expressed as a fuzzy system with a time-varying delay including the event-triggering variable. Under these considerations, a novel proportional-plus-integral (PI) event triggering condition is proposed to alleviate network allocation. Based time-delay approach, the stability of the filtering error systems is guaranteed by a new Lyapunov Kravoskii functional and by employing generalized free-weighting matrix integral inequality. Furthermore, an affine matched membership based distributed-filter (AMDF) is designed to improve the H ∞ performance, utilizing affine transformed membership function as a membership function of fuzzy filter. The affine matched membership function relaxes the parameterized stability condition due to the deviation bounds of sampled fuzzy membership function between consecutive sampling times. To show the effectiveness of proposed method, the results are compared with the unused ones. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the problem of stability analysis for static neural networks with interval time-varying delays is considered. By the consideration of new augmented Lyapunov functionals, new and improved delay-dependent stability criteria to guarantee the asymptotic stability of the concerned networks are proposed with the framework of linear matrix inequalities (LMIs), which can be solved easily by standard numerical packages. The enhancement of the feasible region of the proposed criteria is shown via two numerical examples by the comparison of maximum delay bounds. [Copyright &y& Elsevier]

Abstract: In this paper, the problem of performance and stability analysis for linear systems with interval time-varying delays is considered. First, by constructing a newly augmented Lyapunov–Krasovskii functional which has not been proposed yet, an improved performance criterion with the framework of linear matrix inequalities (LMIs) is introduced. Next, the result and method are extended to the problem of a delay-dependent stability criterion. Finally, numerical examples are given to show the superiority of proposed method. [Copyright &y& Elsevier]

Abstract: This paper presents new delay-dependent synchronization criteria for fuzzy complex dynamical networks with interval time-varying delays. By construction of a suitable Lyapunov–Krasovskii’s (L–K) functional and utilization of Finsler’s lemma, new synchronization criteria for the networks are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. One numerical example is given to illustrate the effectiveness of the proposed methods. [Copyright &y& Elsevier]

Abstract: This paper considers the synchronization problem for coupled neural networks with interval time-varying delays and leakage delay. By construction of a suitable Lyapunov–Krasovskii’s functional and utilization of Finsler’s lemma, novel delay-dependent criteria for the synchronization of the networks are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed methods. [Copyright &y& Elsevier]

Abstract: In this paper, the problem of guaranteed cost synchronization for a complex network is investigated. In order to achieve the synchronization, two types of guaranteed cost dynamic feedback controller are designed. Based on Lyapunov stability theory, a linear matrix inequality (LMI) convex optimization problem is formulated to find the controller which guarantees the asymptotic stability and minimizes the upper bound of a given quadratic cost function. Finally, a numerical example is given to illustrate the proposed method. [Copyright &y& Elsevier]

Abstract: This paper proposes an adaptive control method to achieve the lag synchronization between uncertain complex dynamical network having delayed coupling and a non-identical reference node. Unknown parameters of both the network and reference node are estimated by adaptive laws obtained by Lyapunov stability theory. With the estimated parameters, the proposed method guarantees the globally asymptotical synchronization of the network in spite of unknown bounded disturbances. The effectiveness of our work is verified through a numerical example and simulation. [Copyright &y& Elsevier]

Abstract: This paper proposes improved delay-dependent conditions for asymptotic stability of linear systems with time-varying delays. The proposed method employs a suitable Lyapunov–Krasovskii’s functional for new augmented system. Based on Lyapunov method, delay-dependent stability criteria for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various optimization algorithms. Three numerical examples are included to show that the proposed method is effective and can provide less conservative results. [Copyright &y& Elsevier]

Abstract: This paper considers the problem of passivity-based controller design for Hopfield neural networks. By making use of a convex representation of nonlinearities, a feedback control scheme based on passivity and Lyapunov theory is presented. A criterion for existence of the controller is given in terms of linear matrix inequality (LMI), which can be easily solved by a convex optimization problem. An example and its numerical simulation are given to show the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper considers synchronization of a class of time-delayed chaotic systems with external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, the dynamic feedback controller is established to not only guarantee synchronization between derive and response systems, but also reduce the effect of external disturbance to an norm constraint. Then, a criterion for existence of the controller is given in terms of LMIs. Finally, a numerical simulation is presented to show the effectiveness of the proposed chaos synchronization scheme. [Copyright &y& Elsevier]

Abstract: In the paper, the global asymptotic stability of equilibrium is considered for continuous bidirectional associative memory (BAM) neural networks of neutral type by using the Lyapunov method. A new stability criterion is derived in terms of linear matrix inequality (LMI) to ascertain the global asymptotic stability of the BAM. The LMI can be solved easily by various convex optimization algorithms. A numerical example is illustrated to verify our result. [Copyright &y& Elsevier]

• Polynomially sampled parameter dependent controller is proposed to stabilize the sampled-data LPV system with a larger maximum sampling interval. • An exponential stabilization condition is derived by using a new polynomially parameter dependent Lyapunov function with looped functionals. • The derived exponential stabilization condition is represented as a sum of squares condition which provides a feasible solution that guarantees global optimality. • The proposed method is applied in the numerical example and compared with other methods to show the effectiveness of the proposed method. This paper proposes a polynomially sampled parameter dependent controller design for sampled-data linear parameter varying (LPV) systems. The goal of this study is to design a controller which exponentially stabilizes the system with a larger maximum sampling interval. To achieve this, we utilize the information of the parameters in the controller part. The proposed controller is dependent on the polynomials with respect to the sampled parameters, which is more effective to stabilize the system with a larger maximum sampling interval. To design the controller, an exponential stabilization condition is derived from a new Polynomially Parameter Dependent Quadratic Lyapunov Function with Looped-Functionals (PPDQLLF) which is dependent on the parameters of a plant. The derived condition is represented in terms of the linear matrix inequality (LMI) and it is formulated as sum of squares (SOS) conditions to obtain feasible solutions. The effectiveness of the proposed method is shown by the simulation results of numerical examples. [ABSTRACT FROM AUTHOR]

• This paper proposes a new stability analysis method for time delay systems by using an augmented zero equality. • An improved stability condition of systems is introduced by the use of Finsler's Lemma and an augmented zero equality. • In numerical examples, the maximum bounds of time-delay demonstrate the superiority of the proposed method. This work focuses the delay-dependent stability problem for linear systems with time-varying delays. By composing a suitable augmented Lyapunov–Krasovskii functionals, using recent developed integral inequality and choosing newly states, a set of sufficient conditions for stability condition is induced within framework of linear matrix inequalities (LMIs). To enhance the feasible region of stability, single augmented zero equality is established with the augmented state vectors for the first time and the equality constraint is incorporated into a simple stability criterion by utilizing Finsler's lemma. The comparison of maximum bounds of time-delay with various results proposed by recent studies will be conducted in numerical examples to demonstrate the superiority of the theorems presented by this paper. [ABSTRACT FROM AUTHOR]