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In the framework of sampled-data control, this paper deals with the lag synchronization of chaotic neural networks with time delay meanwhile taking the impulsive control into account. By constructing a proper Lyapunov function and employing the impulsive control theory, some sufficient conditions for lag synchronization of the addressed chaotic neural networks are derived in terms of linear matrix inequalities (LMIs). The hybrid controller including sampled-data controller and impulsive controller is designed based on the established LMIs. A numerical example is provided to demonstrate the effectiveness and advantage of the obtained results.

This paper proposes an adaptive fault-tolerant control method for Markovian jump systems in the presence of actuator fault, unknown dead zone, and external disturbance. There is no prior knowledge of the exact model of the actuator fault. The uncertainty due to the actuator fault and unknown dead zone is tackled by the adaptive rules in the proposed control method. The actuator fault is assumed to be the partial loss of effectiveness. The stochastic stability of the entire system is assured through coupled linear matrix inequalities (LMIs) despite no prior knowledge of actuator fault, dead zone, and external disturbance. The simulation results have validated the merit and efficiency of this proposed control method.

Stability of a standalone hybrid power system (HPS) in a smart grid is always a challenging task. Further, the operational stability of the power system depends on the associated communication infrastructure. Therefore, it is always crucial to pick up a controller that can assure system's stability along with performance, despite disturbances like (load and input wind variations) with communication delays. Present study focuses on reactive power management and voltage stability issues of an isolated HPS. The stability aspects of HPS are improved through reactive power compensation, by custom power devices like static var compensator. The control aspects of SVC as well as the whole hybrid system are taken care by H∞ linear matrix inequalities approach. Further, H-infinity control, Lyapunov stability along with linear matrix inequalities techniques estimate the delay boundary of controllers. The iterative performance of the proportional–integral–derivative controllers, and robust H∞ damping controller of the HPS, are designed through LMI approach. Later experimental study of the HPS is done, with a prototype model in dSPACE real-time control environment. In this case, dSPACE 1104 is added for data acquisition and control. Adaptability and robustness of the proposed controllers are verified under fluctuating loads and uncertain wind power input.

This paper discusses the synchronization problem for a class of reaction–diffusion neural networks with Dirichlet boundary conditions. Unlike other studies, a sampled-data controller with stochastic sampling is designed in order to synchronize the concerned neural networks with reaction–diffusion terms and time-varying delays, where m sampling periods are considered whose occurrence probabilities are given constants and satisfy the Bernoulli distribution. A novel discontinuous Lyapunov–Krasovskii functional with triple integral terms is introduced based on the extended Wirtinger’s inequality. Using Jensen’s inequality and reciprocally convex technique in deriving the upper bound for the derivative of the Lyapunov–Krasovskii functional, some new synchronization criteria are obtained in terms of linear matrix inequalities. Numerical examples are provided in order to show the effectiveness of the proposed theoretical results.

This paper investigates the mean-square stability of uncertain time-delay stochastic systems driven by G-Brownian motion, which are commonly referred to as G-SDDEs. To derive a new set of sufficient stability conditions, we employ the linear matrix inequality (LMI) method and construct a Lyapunov–Krasovskii function under the constraint of uncertainty bounds. The resulting sufficient condition does not require any specific assumptions on the G-function, making it more practical. Additionally, we provide numerical examples to demonstrate the validity and effectiveness of the proposed approach.

In this paper, a hybrid controller with a sampled data control is investigated to achieve finite-time master–slave synchronization of delayed fractional-order neural networks (DFONNs). A Lyapunov-Krasovskii functional is constructed to obtain the sufficient conditions that incorporate delay information. For the first time, the asymptotic stability of the error system is guaranteed in a finite-time using the inequality technique and a sampled-data hybrid controller. The obtained conditions are expressed via linear matrix inequality. Notably, the proposed approach outperforms existing methods, demonstrating improved results in a comparative analysis. An explicit formula is utilized to calculate the settling time, which is significantly influenced by the fractional order$$0<\\beta \\le 1$$0 < β ≤ 1 . The superior performance of the proposed control method is evident, showcasing its effectiveness through numerical simulations and addressing the synchronization problem in DFONNs.

A control design for a linear large-scale interconnected system composed of identical subsystems is presented in this paper. The control signal of all subsystems is sampled. For different subsystems, the sampling times are not identical. Nonetheless, it is assumed that a bound exists for the maximal sampling time. The control algorithm is designed using the Wirtinger inequality, and the non-fragile control law is proposed. The size of the linear matrix inequalities to be solved by the proposed control algorithm is independent of the number of subsystems composing the overall system. Hence, the algorithm is computationally effective. The results are illustrated by two examples. The first example graphically illustrates the function of the proposed algorithm while the second one compares with a method for stabilizing a large-scale system obtained earlier, thus illustrating the improved capabilities of the presented algorithm.

Addressed in this paper is the reachable set estimation (RSE) problem for fuzzy‐model‐based leader‐follower multi‐agent systems with time‐varying delays and false data injection attacks. First, the aperiodic sampled‐data control is designed for the follower agents with randomly occurring false data injection attacks. Then, using the Kronecker product, the error system between the leader and the follower is obtained in a compact general form. Next, a novel Lyapunov‐Krasovskii functional is constructed with the knowledge of sampling patterns and time‐varying delays. In the framework of linear matrix inequalities, sufficient consensus conditions are determined from the H∞ $H_\\infty$performance index and Lyapunov theory to guarantee that its reachable set is enclosed by an ellipsoid in the existence of bounded perturbations. In the end, the Duffing Van der Pol oscillator and the single‐link robot arm models are employed to validate the derived theoretical results. The reachable set estimation problem is considered for the first time for leader‐follower fuzzy MASs with time‐varying delays and bounded external disturbances. The aperiodic sampled‐data control is designed for all the follower agents with the information from the leader. Moreover, the Bernoulli distribution is used for modeling the randomly occurring false data injection attacks in the controller actuator channels. The proposed theoretical findings are validated by two practical examples, that is, Duffing Van der Pol oscillator and single‐link robot arm model.

This paper presents an improved equivalent-input-disturbance (EID) approach to deal with periodic disturbances. The approach has two degrees of freedom. One is an improved EID compensator, in which a repetitive controller is inserted in this study. The other is a conventional servo system for a reference input. The improved EID compensator estimates and compensates for periodic disturbances without steady-state error, and the servo system ensures a satisfactory tracking performance. The improved EID compensator is designed using the linear-matrix-inequality (LMI) method. Three parameters in an LMI are selected using the particle-swarm-optimization (PSO) algorithm. The state-feedback gain of the conventional servo system is designed using the linear-quadratic-regulator (LQR) method. Simulation results of a rotational control system demonstrate the validity of the approach and its advantage over others.

In the paper, observer-based sliding mode control (SMC) for fractional order singular fuzzy (FOSF) systems with order 0 < α < 1 is studied. The non-fragile FOSF observer is designed to reconstruct the unmeasured states, and a novel fractional order integral sliding function is formulated. Then, the admissibility condition of the FOSF error system is derived, based on the linear matrix inequality (LMI) approach. By using the singular value decomposition approach, the strict LMI-based admissibility condition is improved. Based on the fractional order Lyapunov function and sliding surface, the fractional order SMC is constructed to ensure the reachability of the sliding surface. Two examples are given to illustrate the effectiveness of the methods proposed in the paper.