Linear matrix inequality approach to exponential synchronization of a class of chaotic neural networks with time-varying delays

In this paper, a synchronization scheme for a class of chaotic neural networks with time-varying delays is presented. This class of chaotic neural networks covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks, and bidirectional associative memory networks. The obtained criteria are expressed in terms of linear matrix inequalities, thus they can be efficiently verified. A comparison between our results and the previous results shows that our results are less restrictive.

On stabilization for a class of nonlinear stochastic time-delay systems:a matrix inequality approach

This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.

Linear matrix inequality approach for synchronization control of fuzzy cellular neural networks with mixed time delays

Fuzzy cellular neural networks （FCNNs） are special kinds of cellular neural networks （CNNs）. Each cell in an FCNN contains fuzzy operating abilities. The entire network is governed by cellular computing laws. The design of FCNNs is based on fuzzy local rules. In this paper, a linear matrix inequality （LMI） approach for synchronization control of FCNNs with mixed delays is investigated. Mixed delays include discrete time-varying delays and unbounded distributed delays. A dynamic control scheme is proposed to achieve the synchronization between a drive network and a response network. By constructing the Lyapunov-Krasovskii functional which contains a triple-integral term and the free-weighting matrices method an improved delay-dependent stability criterion is derived in terms of LMIs. The controller can be easily obtained by solving the derived LMIs. A numerical example and its simulations are presented to illustrate the effectiveness of the proposed method.

On absolute stability of Lur'e control systems with multiple non-linearities using linear matrix inequalities

Necessary and suffcient conditions for the existence of a Lyapunov function in the Lur ’ e form to guarantee the absolute stability of Lur’ e control systems with multiple non-linearities are discussed in this paper. It simplifies the existence problem to one of solving a set of linear matrix inequalities (LMIs). If those LMIs are feasible, free parameters in the Lyapunov function, such as the positive definite matrix and the coefficients of the integral terms, are given by the solution of the LMIs. Otherwise, this Lyapunov function does not exist. Some sufficient conditions are also obtained for the robust absolute stability of uncertain systems. A numerical example is provided to demonstrate the effectiveness of the proposed method.

Linear matrix inequality approach for robust stability analysis for stochastic neural networks with time-varying delay

This paper studies the problem of linear matrix inequality （LMI） approach to robust stability analysis for stochastic neural networks with a time-varying delay. By developing a delay decomposition approach, the information of the delayed plant states can be taken into full consideration. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, new delay-dependent stability criteria are obtained in terms of LMIs. The proposed results prove the less conservatism, which are realized by choosing new Lyapunov matrices in the decomposed integral intervals. Finally, numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI method.

Event-Triggered Finite-Time H∞ Filtering for Discrete-Time Nonlinear Stochastic Systems

This paper addresses the problem of event-triggered finite-time H∞ filter design for a class of discrete-time nonlinear stochastic systems with exogenous disturbances. The stochastic Lyapunov-Krasoviskii functional method is adopted to design a filter such that the filtering error system is stochastic finite-time stable (SFTS) and preserves a prescribed performance level according to the pre-defined event-triggered criteria. Based on stochastic differential equations theory, some sufficient conditions for the existence of H∞ filter are obtained for the suggested system by employing linear matrix inequality technique. Finally, the desired H∞ filter gain matrices can be expressed in an explicit form.

FUZZY ROBUST H_∞ CONTROL OF UNCERTAIN NONLINEAR SYSTEM WITH TIME-DEALY

This paper addresses the problem of the fuzzy H ∞state feedback control for a class of uncertain nonlinear systems with time delay. The Takagi Sugeno (T S) mo del with time delay and parameter uncertainties is adopted for modeling of nonlinear system. The systematic design procedure for the fuzzy robust controller based on linear matrix inequality (LMI) is given. Some sufficient conditions are derived for the existence of fuzzy H ∞ state feedback controllers such that the closed loop system is asymptotically stable and the effect of the disturbance input on controlled output is reduced to a prescribed level. An example is given to demonstrate the effectiveness of the proposed method.

Static Output Feedback H_∞ Controllers Design for Descriptor Linear Systems Based on LMI

This paper considers the design problem of static output feedback H ∞ controllers for descriptor linear systems with linear matrix inequality (LMI) approach. Necessary and sufficient conditions for the existence of a static output feedback H ∞ controller are given in terms of LMIs. Furthermore, the design method of H ∞ controllers is provided using the solutions to the LMIs.

Optimal Nonlinear Robust Sliding Mode Control of an Excitation System Based on Mixed Linear H_(2)/H_(∞) Matrix Inequalities

In this paper,an optimal nonlinear robust sliding mode control(ONRSMC)based on mixed H_(2)/H_(∞)linear matrix inequalities(LMIs)is designed for the excitation system in a“one machine-infinite bus system”(OMIBS)to enhance system stability.Initially,the direct feedback linearization method is used to establish a mathematical model of the OMIBS incorporating uncertainties.ONRSMC is then designed for this model,employing the mixed H_(2)/H_(∞)LMIs.The chaos mapping-based adaptive salp swarm algorithm(CASSA)is introduced to fully optimize the parameters of the sliding mode control,ensuring optimal performance under a specified condition.CASSA demonstrates rapid convergence and reduced like-lihood of falling into local optima during optimization.Finally,ONRSMC is obtained through inverse transformation,exhibiting the advantages of simple structure,high reliability,and independence from the accuracy of system models.Four simulation scenarios are employed to validate the effectiveness and robustness of ONRSMC,including mechanical power variation,generator three-phase short circuit,transmission line short circuit,and generator parameter uncertainty.The results indicate that ONRSMC achieves optimal dynamic performance in various operating conditions,facilitating the stable operation of power systems following faults.

T-S-fuzzy-model-based quantized control for nonlinear networked control systems

In order to overcome data-quantization, networked-induced delay, network packet dropouts and wrong sequences in the nonlinear networked control system, a novel nonlinear networked control system model is built by the T-S fuzzy method. Two time-varying quantizers are added in the model. The key analysis steps in the method are to construct an improved interval-delay-dependent Lyapunov functional and to introduce the free-weighting matrix. By making use of the parallel distributed compensation technology and the convexity of the matrix function, the improved criteria of the stabilization and stability are obtained. Simulation experiments show that the parameters of the controllers and quantizers satisfying a certain performance can be obtained by solving a set of LMIs. The application of the nonlinear mass-spring system is provided to show that the proposed method is effective.

Delay-dependent H-infinity control for linear descriptor systems with delay in state

A deky-dependent H-infinity control for descriptor systems with a state-delayis investigated. The purpose of the problem is to design a linear memoryless state-feedbackcontroller such that the resulting closed-loop system is regular, impulse free and stable with anH-infinity norm bound. Firstly, a deky-dependent bounded real lemma(BRL) of the time-deky descriptorsystems is presented in terms of linear matrix inequalities(LMIs) by using a descriptor modeltransformation of the system and by taking a new Lyapunov-Krasovsii functional. The introducedfunctional does not require bounding for cross terms, so it has less conservation. Secondly, withthe help of the obtained bounded real lemma, a sufficient condition for the existence of a newdeky-dependent H-infinity state-feedback controller is shown in terms of nonlinear matrixinequalities and the solvability of the problem can be obtained by using an iterative algorithminvolving convex optimization. Finally, numerical examples are given to demonstrate theeffectiveness of the new method presented.

Delay-range-dependent Stability Criterion for Interval Time-delay Systems with Nonlinear Perturbations

In this paper, we consider the problem of robust stability for a class of linear systems with interval time-varying delay under nonlinear perturbations using Lyapunov-Krasovskii （LK） functional approach. By partitioning the delay-interval into two segments of equal length, and evaluating the time-derivative of a candidate LK functional in each segment of the delay-interval, a less conservative delay-dependent stability criterion is developed to compute the maximum allowable bound for the delay-range within which the system under consideration remains asymptotically stable. In addition to the delay-bi-segmentation analysis procedure, the reduction in conservatism of the proposed delay-dependent stability criterion over recently reported results is also attributed to the fact that the time-derivative of the LK functional is bounded tightly using a newly proposed bounding condition without neglecting any useful terms in the delay-dependent stability analysis. The analysis, subsequently, yields a stable condition in convex linear matrix inequality （LMI） framework that can be solved non-conservatively at boundary conditions using standard numerical packages. Furthermore, as the number of decision variables involved in the proposed stability criterion is less, the criterion is computationally more effective. The effectiveness of the proposed stability criterion is validated through some standard numerical examples.

Robust Stability and Stabilization of Discrete Singular Systems with Interval Time-varying Delay and Linear Fractional Uncertainty

The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality （LMI） approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.

Robust model predictive control for discrete uncertain nonlinear systems with time-delay via fuzzy model

An extended robust model predictive control approach for input constrained discrete uncertain nonlinear systems with time-delay based on a class of uncertain T-S fuzzy models that satisfy sector bound condition is presented. In this approach, the minimization problem of the “worst-case” objective function is converted into the linear objective minimization problem in- volving linear matrix inequalities (LMIs) constraints. The state feedback control law is obtained by solving convex optimization of a set of LMIs. Sufficient condition for stability and a new upper bound on robust performance index are given for these kinds of uncertain fuzzy systems with state time-delay. Simulation results of CSTR process show that the proposed robust predictive control approach is effective and feasible.

Robust stability analysis of singular linear system with delay and parameter uncertainty

This paper deals with the problem of robust stability for continuous-time singular systems with state delay and parameter uncertainty. The uncertain singular systems with delay considered in this paper are assumed to be regular and impulse free.By decomposing the systems into slow and fast subsystems,a robust delay-dependent asymptotic stability criteria based on linear matrix inequality is proposed, which is derived by using Lyapunov-Krasovskii functionals, neither model transformation nor bounding for cross terms is required in the derivation of our delay-dependent result. The robust delay-dependent stability criterion proposed in this paper is a sufficient condition. Finally, numerical examples and Matlab simulation are provided to illustrate the effectiveness of the proposed method.

Robust fault detection for a class of nonlinear network control system with communication delay

To investigate a class of nonlinear network control system, a robust fault diagnosis method is presented based on the robust state observer. To access the objective that the designed robust filter is maximally tolerant to disturbances and sensitive to fault, the robustness and stability properties of the fault diagnosis scheme are established rigorously. Using the residual vector, a fault tolerant controller is established in order to guarantee the stability of the closed-loop system, and the controller law can be obtained by solving a set of linear matrix inequalities. Then, some relevant sufficient conditions for the existence of a solution are given by applying Lyapunov stability theory. Finally, a simulation example is performed to show the effectiveness of the proposed approach.

Unknown Input Extended Kalman Filter and Applications in Nonlinear Fault Diagnosis

Unknown input observer is one of the most famous strategies for robust fault diagnosis of linear systems, but studies on nonlinear cases are not sufficient. On the other hand, the extended Kalman filter （EKF） is wellknown in nonlinear estimation, and its convergence as an observer of nonlinear deterministic system has been derived recently. By combining the EKF and the unknown input Kalman filter, we propose a robust nonlinear estimator called unknown input EKF （UIEKF） and prove its convergence as a nonlinear robust observer under some mild conditions using linear matrix inequality （LMI）. Simulation of a three-tank system “DTS200”, a benchmark in process control, demonstrates the robustness and effectiveness of the UIEKF as an observer for nonlinear systems with uncertainty, and the fault diagnosis based on the UIEKF is found successful.

Robust Fuzzy Tracking Control for Nonlinear Networked Control Systems with Integral Quadratic Constraints

This paper investigates the robust tracking control problcm for a class of nonlinear networked control systems （NCSs） using the Takagi-Sugeno （T-S） fuzzy model approach. Based on a time-varying delay system transformed from the NCSs, an augmented Lyapunov function containing more useful information is constructed. A less conservative sufficient condition is established such that the closed-loop systems stability and time-domain integral quadratic constraints （IQCs） are satisfied while both time-varying network- induced delays and packet losses are taken into account. The fuzzy tracking controllers design scheme is derived in terms of linear matrix inequalities （LMIs） and parallel distributed compensation （PDC）. Furthermore, robust stabilization criterion for nonlinear NCSs is given as an extension of the tracking control result. Finally, numerical simulations are provided to illustrate the effectiveness and merits of the proposed method.

Self-triggered Consensus Control for Linear Multi-agent Systems With Input Saturation

In this paper, we study the consensus problem for a class of linear multi-agent systems(MASs) with consideration of input saturation under the self-triggered mechanism. In the context of discrete-time systems, a self-triggered strategy is developed to determine the time interval between the adjacent triggers. The triggering condition is designed by using the current sampled consensus error. Furthermore, the consensus control protocol is designed by means of a state feedback approach. It is shown that the considered multi-agent systems can reach consensus with the presented algorithm. Some sufficient conditions are proposed in the form of linear matrix inequalities(LMIs) to show the positively invariant property of the domain of attraction(DOA). Moreover, some sufficient conditions of controller synthesis are provided to enlarge the volume of the DOA and obtain the control gain matrix. A numerical example is simulated to demonstrate the effectiveness of the theoretical analysis results.