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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.

Since March 2001, a special class of recurrent neural networks termed the Zhang neural network (ZNN) has been proposed by Zhang and co-workers for solving online a rich repertoire of time-varying problems. By extending Zhang et al.'s design formula (or say, the ZNN design formula), a (new) variant of the ZNN design formula is proposed and investigated in this paper, which is also based on a matrix/vector-valued indefinite error function. In addition, by employing such a novel design formula, a new variant of the ZNN (NVZNN) is proposed, developed and investigated for online solution of time-varying linear inequalities (LIs). The resultant NVZNN models are depicted in implicit dynamics and methodologically exploit the time-derivative information of time-varying coefficients. Computer simulation results further demonstrate the novelty, efficacy and superiority of the proposed NVZNN models for solving online time-varying LIs.

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 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.

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.

Linear variable parameter systems (LPV) are a very special class of nonlinear systems, which are suitable for controlling dynamic systems with parameter changes. Therefore, in this thesis, the problem of using variable parameter linear systems for controller design and stability analysis is raised. A designed controller must be able to reduce the adverse effects of disturbances in the output, for this purpose, in this research, by creating a compromise between the two functions of H 2 and H ∞ and combining them with the anticipatory control of the resistant model, a suitable method can be used to eliminate the effect A disturbance was achieved. The controller designed in this research, while stabilizing the system, in the presence of external disturbance, reduces the effect of external disturbance on the output under the control of the system. In general, the purpose of presenting this research is to provide an effective algorithm for controlling a variable parameter linear system with disturbance using the robust model predictive control method, which method presented in this thesis is based on solving the linear matrix inequality, also the proposed method has the ability to consider It has different restrictions on system states and system output. All the results obtained in different sections, including stability analysis, controller performance analysis, are shown using several validated practical examples and their effectiveness. In this thesis, solving optimization problems in the environment is done, as well as the case solvers. It is used to obtain auxiliary and controlling matrices.

In this paper, we exploit the sliding mode control problem for a fluid power electrohydraulic actuator (EHA) system. To characterize the nonlinearity of the friction, the EHA system is modeled as a linear system with a system uncertainty. Practically, it is assumed that the system is also subject to the load disturbance and the external noise. An integral sliding mode controller is proposed to design. The advanced techniques such as the H ∞ control and the regional pole placement are employed to derive the optimal feedback gain which can be calculated by solving a necessary and sufficient condition in the form of linear matrix inequality. A sliding mode control law is developed such that the sliding mode reaching law is satisfied. Simulation and comparison results show the effectiveness of the proposed design method.

The paper focuses on the admissibility problem of descriptor fractional-order systems (DFOSs). The alternate admissibility criteria are addressed for DFOSs with order in (0,2) which involve a non-strict linear matrix inequality (LMI) method and a strict LMI method, respectively. The forms of non-strict and strict LMIs are brand new and distinguished with the existing literature, which fills the gaps of studies for admissibility. These necessary and sufficient conditions of admissibility are available to the order in (0,2) without separating the order ranges into (0,1) and [1,2). Based on the special position of singular matrix, the non-strict LMI criterion has an advantage in handling the DFOSs with uncertain derivative matrices. For the strict LMI form, a method involving least real decision variables is derived which is more convenient to process the practical solution. Three numerical examples are given to illustrate the validity of the proposed results.

This paper addresses the issue of cooperative control concerning the output synchronization of the linear time-invariant multi-input multi-output multi-agent system i.e., multi-unmanned aerial vehicle (a swarm of the drone), by designing observer-based consensus protocol with directed communication topology. Considering the leader following consensus tracking problem, an observer-based protocol is designed to obtain desirable output synchronization. The protocol design consists of a local observer for the leader drone and a distributed observer for the follower drones. Observer gains are optimized through a multi-step algorithm based on linear quadratic regulator controller and linear matrix inequalities. Most of the existing literature on cooperative control considers full state information for the controller as well as observer design. However, the protocol for the controller and observer design for consensus tracking of multi-unmanned aerial vehicles presented in this paper considers that only the relative partial states information from the corresponding neighboring drones are utilized. The designed algorithm is robust and guarantees that all the states of follower drones track the states of the leader drone and the consensus is achieved asymptotically even in the presence of external disturbances. Finally, considering the ideal and perturbed system, the efficacy of the analytical results are illustrated by comparative analysis using numerical simulations.