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Summary: With the aid of a proportional integral framework, the presented article focuses on the problems of finite‐time boundedness and fault estimation for Takagi–Sugeno fuzzy singular systems subject to time delays, faults and external disturbances. To commence, we conjure up a fuzzy‐dependent intermediate variable and from thereon, a proportional integral‐based fuzzy intermediate estimator is constructed. Moreover, the constructed estimator precisely facilitates for estimating the fault signals and system states in simultaneously. Besides this, the integral term in the proportional integral estimator offers greater design flexibility and higher resilience. Secondly, an intermediate estimator‐based fault‐tolerant control is devised by availing the information from the proportional integral‐based fuzzy intermediate estimator, which aids in effectively compensating the faults arising in the system. Subsequently, by setting up an appropriate Lyapunov–Krasovskii functional, the set of adequate requirements asserting the finite‐time boundedness with the endorsed mixed H∞$$ {H}_{\infty } $$ and passivity performance index is established in terms of linear matrix inequalities. After that, an explicit framework for the requisite gain matrices can be found forth basing on the formed linear matrix inequality criteria. Ultimately, simulation findings are supplied to evaluate the utility and applicability of the theoretical insights. [ABSTRACT FROM AUTHOR]

The robust stabilization problem for singular fractional order time delay T-S fuzzy systems with nonlinearities and unknown external disturbances is addressed in this paper. An equivalent-input-disturbance (EID) estimator is used to estimate the impact of external disturbances and nonlinearities on the system output. Based on this EID approach, a dynamic compensator is designed to solve the stabilization problem of the considered system. Moreover, by considering a relevant Lyapunov-Krasovskii functional candidate and by using Lyapunov technique, the stability conditions in terms of LMIs are acquired for the considered closed-loop system. At last, to validate the effectiveness of the proposed result, two numerical examples are provided. [ABSTRACT FROM AUTHOR]

This paper establishes an observer-based finite-time non-fragile load frequency control design using electric vehicles for power systems with modeling uncertainties and external disturbances. A state space representation of the addressed power systems together with dynamic interactions of electric vehicles is formulated. A full-order observer-based non-fragile controller is designed to ensure finite-time boundedness and satisfactory finite-time H ∞ performance of the considered system. By constructing an augmented Lyapunov–Krasovskii functional and employing Wirtinger-based integral inequality, the required conditions are obtained in terms of linear matrix inequalities. The desired non-fragile load frequency control law is presented via the observer-based feedback approach. Simulations are given to show the effectiveness of the proposed control scheme. • A load frequency controller with multiple time delays is proposed for power systems. • The proposed method does not require any information on states of the power system. • Delay-dependent stability criterion is developed for the resulting closed-loop system. [ABSTRACT FROM AUTHOR]

Abstract This paper focuses on the problem of finite-time consensus of linear multi-agent systems with input time-varying delay by employing a non-fragile control scheme, where the network topology of the communication process among agents is subject to a switching directed graph. The main intention of this paper is to propose a non-fragile controller design protocol that guarantees the finite-time stability of the resulting closed-loop system even in the presence of time-varying delay in the input channel. Sufficient conditions for the solvability of such a problem are obtained by using the Lyapunov–Krasovskii stability theory, the algebraic graph theory and some integral inequalities. Based on the obtained conditions, an explicit expression of the desired non-fragile control gain matrix is then presented. Finally, an illustrative example is given to exhibit the applicability and effectiveness of the proposed finite-time consensus control design method. [ABSTRACT FROM AUTHOR]

This paper addresses the issue of reliable load frequency control design of an uncertain multi-area power system with constant time delays and disturbances via non-fragile sampled-data control approach. In particular, the parameter uncertainties are assumed to be randomly occurring which are described by the Bernoulli distributed sequences. By constructing a suitable Lyapunov-Krasovskii functional together with Wirtinger-based inequality, a new set of sufficient conditions in terms of linear matrix inequalities is obtained to ensure the asymptotic stability and extended dissipativity of the multi-area power system not only when all actuators are operational, but also in case of some actuator failures. Finally, simulation results are conducted to validate the effectiveness of the proposed control design technique. [ABSTRACT FROM AUTHOR]

This paper examines the robust consensus problem of nonlinear multi-agent systems via a resilient controller subject to switching topology, wherein the effect of uncertainty in the form of additive perturbations and a randomly varying communication delay is considered in the control design. In particular, a directed graph is used to describe the interaction topology of the addressed multi-agent system and a stochastic variable obeying the Bernoulli distributed white sequences is incorporated to represent the randomness of delay. By utilizing the Lyapunov’s direct method and some matrix operations, a sufficient condition for mean-square asymptotic consensus of the addressed system is derived. Subsequently, the explicit characterization of the resilient control gain is obtained by means of linear matrix inequalities that can be effectively solved by using the ideas of convex optimization. An academic example is eventually presented to illustrate the significance and potency of the proposed control design strategy. [ABSTRACT FROM AUTHOR]

In this paper, the output tracking control problem for a class of switched nonlinear systems with multiple time-varying delays is studied based on equivalent-input-disturbance (EID) approach. More precisely, with the use of suitable Lyapunov-Krasovskii functional together with average dwell-time technique, an output feedback tracking controller is designed which makes that the states of resulting system can asymptotically track the desired trajectory. Further, the EID estimator is implemented to reject both matched and unmatched disturbances effectively without requiring any prior knowledge of the disturbances. Simulation results are presented to illustrate the effectiveness and potential of the developed EID-based output tracking control design technique. The results reveal the fact that the tracking controller based on EID provides a better tracking performance than the feedback controller based on sliding mode technique. [ABSTRACT FROM AUTHOR]

This paper develops the repetitive control scheme for state tracking control of uncertain stochastic time-varying delay systems via equivalent-input-disturbance approach. The main purpose of this work is to design a repetitive controller to guarantee the tracking performance under the effects of unknown disturbances with bounded frequency and parameter variations. Specifically, a new set of linear matrix inequality (LMI)-based conditions is derived based on the suitable Lyapunov–Krasovskii functional theory for designing a repetitive controller which guarantees stability and desired tracking performance. More precisely, an equivalent-input-disturbance estimator is incorporated into the control design to reduce the effect of the external disturbances. Simulation results are provided to demonstrate the desired control system stability and their tracking performance. A practical stream water quality preserving system is also provided to show the effectiveness and advantage of the proposed approach. [ABSTRACT FROM AUTHOR]

This article studies the reliable robust stabilization problem for a class of uncertain Takagi–Sugeno (TS) fuzzy systems with time-varying delays. The delay factor is assumed to be random delay which belongs to a given interval and parameter uncertainties are considered with linear fractional transformation form. By implementing a proper novel Lyapunov functional together with linear matrix inequality (LMI) approach, a new set of delay-dependent sufficient conditions is derived to guarantee the asymptotic stability of TS fuzzy system with a prescribed H ∞ performance index. Further, a reliable robust H ∞ control design with an appropriate gain matrix has been derived to achieve the robust asymptotic stability for uncertain TS fuzzy system. Further, Schur complement and Jensen's integral inequality are used to simplify the derivation in the main results. The set of sufficient conditions is established using the relationship among the random time-varying delay and its lower and upper bounds, which can be easily solved by MATLAB LMI toolbox. Finally, an illustrative example based on the truck-trailer model is provided to show the effectiveness of the proposed new design technique. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of robust $$L_2{-}L_\infty $$ control in delta domain for a class of Takagi-Sugeno (TS) fuzzy systems with interval time-varying delays and disturbance input. In particular, the system under study involves state time delay, uncertainties and fast sampling period $$\mathcal {T}$$ . The main aim of this work was to design a $$L_2{-}L_\infty $$ controller such that the proposed TS fuzzy system is robustly asymptotically stable with a $$L_2{-}L_\infty $$ prescribed performance level $$\gamma >0$$ . Based on the proper Lyapunov-Krasovskii functional (LKF) involving lower and upper bound of time delay and free-weighting technique, a new set of delay-dependent sufficient conditions in terms of linear matrix inequalities (LMIs) are established for obtaining the required result. The result reveals that the asymptotic stability is achieved quickly when the sampling frequency is high. Finally, a numerical example based on the truck-trailer model is given to demonstrate the effectiveness and potential of the proposed design technique. [ABSTRACT FROM AUTHOR]

Synthesis of control design is an essential part for vehicle suspension systems. This paper addresses the issue of robust reliable H control for active vehicle suspension system with input delays and linear fractional uncertainties. By constructing an appropriate Lyapunov-Krasovskii functional, a set of sufficient conditions in terms of linear matrix inequalities (LMIs) are derived for ensuring the robust asymptotic stability of the active vehicle suspension system with a H∞ disturbance attenuation level y. In particular, the uncertainty appears in the sprung mass, unsprung mass, damping and stiffness parameters are assumed in linear fractional transformation (LFT) formulations. More precisely, the designed controller is presented in terms of the solution of LMIs which can be easily checked by MATLAB-LMI toolbox. Finally, a quarter-car suspension model is considered as an example to illustrate the effectiveness and applicability of the proposed control strategy. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of robust stabilization for a class of discrete-time stochastic neural networks with randomly occurring discrete and distributed time-varying delays. More precisely, the neuron activation functions are assumed to be more general and satisfy sector-like nonlinearities. Moreover, the effects of both variation range and probability distribution of mixed time-delays are taken into consideration in the proposed problem. The main objective of this paper is to design a state feedback reliable H ∞ controller such that for all admissible uncertainties as well as actuator failure cases, the resulting closed-loop form of considered neural network is robustly asymptotically stable while satisfying a prescribed H ∞ performance constraint. Linear matrix inequality approach together with proper construction of Lyapunov–Krasovskii functional is employed for obtaining delay dependent sufficient conditions for the existence of robust reliable H ∞ controller. The obtained results are formulated in terms of linear matrix inequalities (LMIs) which can be easily solved by using the MATLAB LMI toolbox. Finally, a numerical example with simulation results is provided to illustrate the effectiveness of the obtained control law and less conservativeness of the proposed results. [ABSTRACT FROM AUTHOR]

The problem of robust reliable stabilization against actuator failures for a class of uncertain nonlinear neutral systems with time-varying delays is considered. Based on a new Lyapunov—Krasovskii functional, by employing linear matrix inequality technique and free weighting matrix approach, we derived a set of sufficient conditions for the existence of a reliable controller. The derived controller is applied for the robust stabilization of the nonlinear neutral system in the presence of known actuator failure matrix and uncertainties. Further, the results are extended to study the stabilization of neutral systems with unknown actuator failure matrix. The failure of actuators are considered by variables, which are varying in a given interval. The developed theoretical results are established in the form of linear matrix inequalities, which can be easily solved via standard numerical software. Finally, two numerical examples are presented to demonstrate the validity and less conservatism of the obtained results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the asymptotic stability issue for a class of stochastic Takagi-Sugeno (TS) fuzzy systems with time-varying delays. Then, by utilizing a delay-fraction ing method, the stochastic analysis theory combined with the matrix inequality technique, a new set of sufficient condition in terms of linear matrix inequalities is pre-sented which ensures the asymptotic stability of the stochastic TS fuzzy systems with time-delays. The results obtained in this paper are delay-dependent in the sense that they depend on not only the lower bound but also the upper bound of the time-varying delay. Numerical examples are given to illustrate the effectiveness and less conservativeness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we study the passivity analysis for a class of neutral-type BAM neural networks with time-varying delays and randomly occurring uncertainties as well as generalized activation functions. Linear matrix inequality (LMI) approach together with the construction of proper Lyapunov–Krasovskii functional involving triple integrals and augmented type constraint is implemented to derive a new set of sufficient conditions for obtaining the required result. More precisely, first we derive the passivity condition for BAM neural networks without uncertainties and then the result is extended to the case with randomly occurring uncertainties. In particular, the presented results depend not only upon discrete delay but also distributed time varying delay. The obtained passivity conditions are formulated in terms of linear matrix inequalities that can be easily solved by using the MATLAB-LMI toolbox. Finally, the effectiveness of the proposed passivity criterion is demonstrated through numerical example. [Copyright &y& Elsevier]

This paper addresses the problem of passivity analysis issue for a class of fuzzy bidirectional associative memory (BAM) neural networks with Markovian jumping parameters and time varying delays. A set of sufficient conditions for the passiveness of the considered fuzzy BAM neural network model is derived in terms of linear matrix inequalities by using the delay fractioning technique together with the Lyapunov function approach. In addition, the uncertainties are inevitable in neural networks because of the existence of modeling errors and external disturbance. Further, this result is extended to study the robust passivity criteria for uncertain fuzzy BAM neural networks with time varying delays and uncertainties. These criteria are expressed in the form of linear matrix inequalities (LMIs), which can be efficiently solved via standard numerical software. Two numerical examples are provided to demonstrate the effectiveness of the obtained results. [Copyright &y& Elsevier]

Abstract: This paper provides a novel result on robust exponential stability for a class of uncertain discrete-time switched fuzzy neural networks (DSFNNs) with time-varying delays and parameter uncertainties. By implementing an average dwell time approach with a new Lyapunov–Krasovskii functional, we obtain some delay-dependent sufficient conditions guaranteeing the robust exponential stability of the considered switched fuzzy neural networks. In other words, a class of switching signals specified by the average dwell time is identified to guarantee the exponential stability of the considered DSFNNs. The obtained conditions are formulated in terms of Linear Matrix Inequalities (LMIs) which can be easily verified via the LMI toolbox. Finally, numerical examples with simulation results are provided to illustrate the applicability and usefulness of the obtained results. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the problem of robust stabilization and control for a class of discrete-time switched neural networks with various activation functions and mixed time delays. By using the average dwell time approach together with the multiple Lyapunov function technique, we propose a state feedback controller to guarantee that the switched neural networks is robustly exponentially stable with the disturbance attenuation level γ>0 about its equilibrium point for all admissible uncertainties. The obtained results are formulated in terms of linear matrix inequalities (LMIs) which can be easily verified by the MATLAB LMI control toolbox. Finally, numerical examples with simulation result are given to illustrate the effectiveness and applicability of the obtained results. [Copyright &y& Elsevier]

In the last few years, the H∞ control problem has attracted much attention because of its both practical and theoretical importance. This study presents a robust H∞ control design approach for a class of uncertain discrete-time stochastic neural networks with time-varying delays. The neural network under consideration is subject to time-varying and norm bounded parameter uncertainties. For the robust stabilisation problem, a state feedback controller is designed to ensure global robust stability of the closed-loop form of neural network about its equilibrium point for all admissible uncertainties. In addition, to the requirement of the global robust stability, a prescribed H∞ performance level for all delays to satisfy both the lower bound and upper bound of the interval time-varying delay is required to be obtained. Through construction of a new Lyapunov-Krasovskii functional, a robust H∞ control scheme is presented in terms of linear matrix inequalities (LMIs). The controller gains can be derived by solving a set of LMIs. Finally, numerical examples with simulation results are given to illustrate the effectiveness of the developed theoretical results. [ABSTRACT FROM AUTHOR]

In this article, the problem of robust stability and stabilisation for a class of uncertain neutral systems with discrete and distributed time delays is considered. By utilising a new Lyapunov functional based on the idea of delay partitioning approach, we employ the linear matrix inequality technique to derive delay-dependent criteria which ensures the robust stability of uncertain neutral systems. The obtained stability conditions are formulated in terms of linear matrix inequalities that can easily be solved by using standard software packages. Further, the result is extended to study the robust stabilisation for uncertain neutral systems with parameter uncertainties. A state feedback controller is proposed to guarantee the robust asymptotic stabilisation for uncertain systems and the controller is constructed in terms of the solution to a set of matrix inequalities. Finally, numerical examples are presented to illustrate the effectiveness and conservatism of the obtained results. It is shown that the results developed in this article can tolerate larger allowable delay than some existing works in the literature. Further, it is proved that the proposed criterion is also computationally less conservative when compared to some existing results. [ABSTRACT FROM PUBLISHER]

Abstract: This paper is concerned with the problem of passivity analysis for a class of Cohen–Grossberg fuzzy bidirectional associative memory (BAM) neural networks with time varying delay. By employing the delay fractioning technique and linear matrix inequality optimization approach, delay dependent passivity criteria are established that guarantees the passivity of fuzzy Cohen–Grossberg BAM neural networks with uncertainties. The passivity condition is expressed in terms of LMIs, which can be easily solved by various convex optimization algorithms. Finally, a numerical example is given to illustrate the effectiveness of the proposed result. [Copyright &y& Elsevier]

In this paper, the asymptotic stability for a class of stochastic neural networks with time-varying delays and impulsive effects are considered. By employing the Lyapunov functional method, combined with linear matrix inequality optimization approach, a new set of sufficient conditions are derived for the asymptotic stability of stochastic delayed recurrent neural networks with impulses. A numerical example is given to show that the proposed result significantly improve the allowable upper bounds of delays over some existing results in the literature. [ABSTRACT FROM AUTHOR]

This research delves in addressing the stabilization challenge in linear time-varying delayed systems through the utilization of functional observers (FOs) in feedback control. More precisely, a linear function or functions of the system states are estimated, driven by the available system inputs and outputs. Instead of using traditional methods that estimate the complete set of states, this strategic inclusion enables the estimation of certain functions of the states. The benefit of this novel approach is that it does not require the observed system to be observable. We define stability conditions in terms of linear matrix inequalities, based on the Lyapunov theory. The gain matrices are taken into consideration based on predetermined standards. Finally, we provide numerical illustrations and simulation outcomes to showcase the feasibility and efficiency of our proposed control approach. [ABSTRACT FROM AUTHOR]

In this paper, we formulate and investigate the impulsive synchronization of memristor based bidirectional associative memory (BAM) neural networks with time varying delays. Based on the linear matrix inequality (LMI) approach, the impulsive time dependent results are derived for the exponential stability of the error system, which guarantees the exponential synchronization of the BAM model by means of master–slave synchronization concept. Different from the existing models, an observer (slave system) for the considered BAM neural network in this paper is modeled with time-varying and random impulse moments. Some sufficient conditions are obtained to guarantee the exponential synchronization of the BAM model is derived by using the time-varying Lyapunov function. Simple LMI expressions are proposed to find the feedback controller gains at impulse instants. Finally, a numerical example is presented to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the problem of robust exponential stability analysis for a class of Takagi–Sugeno (TS) fuzzy Cohen–Grossberg neural networks with uncertainties and time-varying delays is investigated. A generalized activation function is used, and the assumptions such as boundedness, monotony and differentiability of the activation functions are removed. By using a Lyapunov–Krasovskii functional and employing the delay fractioning approach, a set of sufficient conditions are established for achieving the required result. The obtained conditions are proposed in terms of linear matrix inequalities (LMIs), so its feasibility can be checked easily via standard numerical toolboxs. The main advantage of the proposed criteria lies in its reduced conservatism which is mainly based on the time delay fractioning technique. In addition to that, a numerical example with simulation results is given to show the effectiveness of the obtained LMI conditions. [Copyright &y& Elsevier]

This paper is concerned with the problem of fault-tolerant control for discrete-time interval type-2 (IT2) fuzzy time delay system with actuator faults under imperfect premise matching. The time-varying delay and actuator fault are first taken into account for the IT2 fuzzy discrete-time systems. The novel IT2 state-feedback controller and the IT2 fuzzy model share different lower and upper membership functions. The fault-tolerant controller is designed to compensate for the effect of faults by stabilizing the closed-loop system under the actuator failures. Furthermore, the standard IT2 state-feedback controller is designed such that the closed-loop system is asymptotically stable and has an H ∞ performance. The obtained conditions of the fault-tolerant controller and the standard IT2 controller can be expressed by the convex optimization problems. A numerical example is presented to show the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the delay-dependent state estimation of neural networks with a mixed time-varying delay is considered. By constructing a suitable Lyapunov–Krasovskii functional with triple integral terms and using Jensen inequality and linear matrix inequality (LMI) framework, the delay-dependent criteria are presented so that the error system is globally asymptotically stable with performance. The activation functions are assumed to satisfy sector-like nonlinearities. The estimator gain matrix for delayed neural networks can be achieved by solving LMIs, which can be easily facilitated by using some standard numerical packages. Finally a numerical example with simulation is presented to demonstrate the usefulness and effectiveness of the obtained results. [Copyright &y& Elsevier]