Free-weighting Matrix Approach Research Articles

Fixed-time consensus control for uncertain heterogeneous multi-agent systems with high-order dynamics and time-varying delay under generic topologies

This article is concerned with the fixed-time control problem of uncertain high-order heterogeneous multi-agent systems with time-varying delays for both directed and undirected topologies. Applying the free-weighting matrix approach, a sliding mode controller is designed through the Lyapunov–Krasovskii functional and the conditions are derived with the help of linear matrix inequalities to attain fixed-time consensus tacking control of such systems. Two numerical simulations are included to verify the capability of the derived control law with respect to different initializations.

Free-Weighting Matrix Approach for Event-Triggered Cooperative Control of Generic Linear Multi-agent Systems: An Application for UAVs

Free-Weighting Matrix Approach for Event-Triggered Cooperative Control of Generic Linear Multi-agent Systems: An Application for UAVs

Asymptotic synchronization of delayed Lur’e systems via non-fragile sampled-data control

This paper is dedicated to investigating the asymptotic synchronization of delayed Lur’e systems via non-fragile aperiodic sampled-data control. Two different kinds of gain fluctuations are taken into consideration. A time-dependent two-sided looped functional is proposed, which makes efficient use of the obtainable information not only of the whole sampling intervals, but also of the nonlinear functions of the considered systems. A criterion on global asymptotic stability is derived by means of the constructed looped functional and using the free-weighting matrix approach. Then, a non-fragile aperiodic sampled-data controller, which allows both additive and multiplicative gain fluctuations, is designed to ensure the asymptotic synchronization based on solutions of a set of linear matrix inequities. Finally, an example with simulations is presented, which shows that the designed controller allows a larger sampling period in comparison with the existing results.

Mittag–Leffler stability and synchronization of neutral-type fractional-order neural networks with leakage delay and mixed delays

In recent years, there have been a lot of studies focusing on the dynamics of fractional-order neural networks (FONNs). One problem is that the standard Lyapunov theory does not apply to fractional-order systems, so these studies rely on the use of Halanay-type lemmas to develop sufficient criteria for certain dynamic properties of FONNs, which frequently results in much more conservative criteria than the ones obtained for integer-order neural networks. The present research uses the Halanay-type lemma in a novel way, in order to obtain less conservative sufficient criteria than previous studies. On the other hand, the previous research only considers FONNs with some types of delays, thus limiting their applicability in real-life scenarios, where possibly many more types of delays are relevant. To address this issue, the paper discusses very general FONNs that include neutral-type delay, leakage delay, time-varying delays, and distributed delay. This is the first time such a general model for the fractional-order scenario has been developed, to our awareness. Three theorems, each based on a distinct Lyapunov-like function, are used to construct sufficient criteria, given in terms of linear matrix inequalities, which ensure, respectively, the Mittag–Leffler stability and synchronization, using two different and general state feedback control schemes, of the proposed networks. The usage of the free weighting matrix approach, among the first times in the context of FONNs, also significantly contributes to reducing the conservatism of the deduced sufficient conditions. One numerical example is provided to illustrate each of the three theorems.

An Enhanced Input-Delay Approach to Sampled-Data Stabilization for Nonlinear Stochastic Singular Systems Based on T-S Fuzzy Models

The sampled-data stabilization problem of nonlinear stochastic singular systems on the basis of the Takagi–Sugeno fuzzy models under variable samplings is discussed in this article. A new piecewise Lyapunov–Krasovskii functional is constructed, which can capture the actual sampling mode’s available features more fully, and an enhanced input-delay method is presented. By using the proper augmented scheme based on the auxiliary vector function, the new mean square admissibility criteria are derived by making good use of the convex combination techniques and the free weighting matrix approach. It is shown that the obtained results in this article contain less conservatism when compared with the existing ones. The superiority and correctness of our results are verified by an application example of a truck–trailer model.

Adaptive event-triggered finite-time [formula omitted] control for fuzzy semi-Markovian jump systems with immeasurable premise variables

This paper addresses the adaptive event-triggered finite-time H∞ control problem of Takagi-Sugeno fuzzy semi-Markovian jump systems with immeasurable premise variables. Firstly, different from some existed works, the restrictions of measurable system states and measurable premise variables of nonlinear plant are removed and the fuzzy observer is designed to estimate unmeasurable system states. Then, a novel adaptive event-triggered scheme is firstly proposed to reduce the number of data transmission while ensuring the reliable system performance. Subsequently, the asynchronous problem about premise variables, namely, the premise variables of fuzzy system are not consistent with premise variables of fuzzy event-triggered controller is dealt with by utilizing an asynchronous method. By applying the delay system method, free-weighting matrix approach and slack matrix variables, novel sufficient conditions are derived to guarantee the finite-time H∞ performance of the closed-loop system, where the nonlinear terms caused by network-induced delay and partly unknown transition rates can be tackled by using suitable method. Finally, the single-link robot arm system is presented to affirm the efficiency of the obtained theoretical results.

Finite-time dissipative synchronization of discrete-time semi-Markovian jump complex dynamical networks with actuator faults

This paper is concerned with the problem of finite-time synchronization for a class of discrete-time semi-Markovian jumping complex dynamical networks (CDNs) with actuator faults based on reliable control. The main aim of this paper is to design a state feedback controller such that the resulting closed-loop system is finite-time synchronized under a prescribed dissipativity performance level even in the presence of actuator failures. Moreover, a stochastic nature followed by Bernoulli distribution is described in the considered networks due to the occurrence of probabilistic nature in time-varying delays. By composing a suitable Lyapunov–Krasovskii functional containing triple summation terms with the aid of Kronecker product properties, Lyapunov stability theory and free weighting matrix approach, sufficient criteria are established in terms of linear matrix inequalities that assure finite-time synchronization and meet the dissipativity performance to the addressed CDNs. The usefulness of the presented design scheme is finally verified by numerical examples.

A new adaptive event-triggered scheme-based finite-time H∞ control for quantized fuzzy semi-Markovian jump systems

ABSTRACT This paper addresses the finite-time control problem of fuzzy semi-Markovian jump systems with quantization and partly unknown transition rates via a new observer-based adaptive event-triggered scheme. Firstly, compared with traditional event-triggered scheme, a new observer-based adaptive event-triggered scheme is designed to reduce the transmission of redundant data and relax the restriction of real system states, which is demonstrated through sufficient comparison experiments in the simulation. Furthermore, by applying the delay system method, free-weighting matrix approach and slack matrix variables, multiple appropriate Lyapunov–Krasovskii functional candidates are constructed to formulate novel sufficient conditions which guarantee the stochastic finite-time performance of the closed-loop system, where the nonlinear terms caused by network-induced delay, quantization and partly unknown transition rates can be tackled by suitable method. Finally, two simulation examples are presented to affirm the efficiency and advantages of the proposed fuzzy control scheme.

Filter Design for Positive T–S Fuzzy Continuous-Time Systems With Time Delay Using Piecewise-Linear Membership Functions

This article focuses on the filtering problem and stability analysis for positive Takagi-Sugeno (T-S) fuzzy systems with time delay under L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -induced performance. Due to the importance of estimation of system states but the few filter design results on positive nonlinear systems, it is an attractive and meaningful topic well worth studying. In order to fully exploit and take advantage of the positivity of positive T-S fuzzy systems, many commonly used methods, for instance free-weighting matrix approach and similarity transformation are probably not suitable for positive systems. To address the hard-nut-to-crack problem, an auxiliary variable is introduced so that the augmentation approach can be employed to carry out the positivity and stability analysis of filtering error systems. In addition, another obstacle that cannot be ignored is the existence of nonconvex terms in the stability and positivity conditions. For getting around this barrier, some iterative linear matrix inequality algorithms have been proposed in the literature. However, considering the weakness that these methods cannot guarantee the convergence to a numerical solution and the iterative process is exhaustive, we present an effective matrix decoupling method to convert the nonconvex conditions into convex ones in this article. Furthermore, a linear copositive Lyapunov function, which incorporates the positivity of system states and time delay at the same time is chosen so that the positivity characteristic of filtering error systems can be captured further. However, because of plenty of valuable information of membership functions being ignored, hence, the obtained results are conservative. For the sake of relaxing the conservativeness, the advanced piecewise-linear membership functions approximate method is utilized to facilitate the stability and positivity analysis. Therefore, the relaxed stability and positivity conditions, which are cast as sum of squares (SOS) are obtained and can be solved numerically. Finally, the effectiveness of the designed fuzzy filtering strategy with satisfying L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -induced performance are demonstrated by a simulation example.

Robust synchronization of uncertain Markovian jumping complex interconnected neural networks via adaptive fault-tolerant control

This article inspects the problem of robust synchronization for uncertain Markovian jumping complex interconnected neural networks with randomly occurring uncertainties and time delays. The uncertainties considered here occur randomly and are assumed to follow certain mutually uncorrelated Bernoulli distributed white noise sequences. The presence of sensor faults may cause degradation or even instability of the entire network. Therefore, control laws are designed with sensor faults to ensure the controlled synchronization of the complex interconnected neural networks. Three types of fault-tolerant controls are designed based on the Lyapunov stability theory and adaptive schemes which include passive and adaptive fault-tolerant control laws. By constructing a new Lyapunov-Krasovskii functional (LKF) and by using Jensen’s inequality with a free-weighting matrix approach, some new delay-dependent synchronization criteria are obtained in terms of linear matrix inequalities (LMIs). By using the Lyapunov stability theory, the existence condition for the adaptive controller that guarantees the robust mean-square synchronization of complex interconnected neural networks in terms of LMIs are derived. Finally, a numerical example is presented to demonstrate the performance of the developed approach.

Quantized control for extended dissipative synchronization of chaotic neural networks: A discretized LKF method

This work focuses on the extended dissipative synchronization problem for chaotic neural networks with time delay under quantized control. The discretized Lyapunov–Krasovskii functional method, in combination with the free-weighting matrix approach, is employed to obtain an analysis result of the extended dissipativity with low conservatism. Then, with the help of several decoupling methods, a computationally tractable design approach is proposed for the needed quantized controller. Finally, two examples are provided to illustrate the usefulness of the present analysis and design methods, respectively.

Distributed consensus control for a group of autonomous marine vehicles with nonlinearity and external disturbances

This paper is concerned with the distributed consensus control for a group of autonomous marine vehicles with nonlinearity and external disturbances via sampled-data communications. First, the kinematical equation of autonomous marine vehicle is established. Second, stability criteria is derived to ensure the stability of autonomous marine vehicles by combining Lyapunov function method and free-weighting matrix approach. Third, a distributed sampled-data control strategy is proposed to achieve the consensus of autonomous marine vehicles by designing suitable control parameters. Numerical simulations are provided to verify the effectiveness of the proposed consensus control approach.

Stochastic Finite-Time H∞ State Estimation for Discrete-Time Semi-Markovian Jump Neural Networks With Time-Varying Delays.

In this article, the finite-time H∞ state estimation problem is addressed for a class of discrete-time neural networks with semi-Markovian jump parameters and time-varying delays. The focus is mainly on the design of a state estimator such that the constructed error system is stochastically finite-time bounded with a prescribed H∞ performance level via finite-time Lyapunov stability theory. By constructing a delay-product-type Lyapunov functional, in which the information of time-varying delays and characteristics of activation functions are fully taken into account, and using the Jensen summation inequality, the free weighting matrix approach, and the extended reciprocally convex matrix inequality, some sufficient conditions are established in terms of linear matrix inequalities to ensure the existence of the state estimator. Finally, numerical examples with simulation results are provided to illustrate the effectiveness of our proposed results.

Event‐triggered synchronisation of Markovian reaction–diffusion inertial neural networks and its application in image encryption

This study investigates the issue of dissipative synchronisation for inertial neural networks with Markovian jumping parameters and reaction–diffusion terms via the event-based control strategy. First, for study convenience, by employing a suitable variable substitution, the original synchronisation error system is transformed to a first-order differential one, and then it is reformed as a compact form. Second, an innovative event-triggered communication scheme that consists of the system's state and its first-order derivatives is proposed, with which the current sampling signal is judged whether should be released. Third, by constructing a novel Lyapunov–Krasovskii functional, and integrating the reciprocally convex combination method, free-weighting matrix approach and Wirtinger-based integral inequality, the dissipative synchronisation criterion that has less conservatism is derived. Finally, two examples are provided, one is a simple numerical example to account for the effectiveness of the main results, the other realises the application of this study in establishing a spatiotemporal chaotic cryptosystem to transmit the encrypted image. Furthermore, the proposed cryptosystem has been illustrated to have obvious advantages of large key space and high security by simulation results.

An event-based interaction method for consensus of multiple complex networks

A consensus criterion for multiple complex networks is proposed in the paper. Based on event-triggered samplers, a projection is employed to select communication instant for various complex systems with the same natural attributes, with that the transmission of information between networks is synchronous. To reduce redundant data in sampling, by utilizing the generalized free-weighting matrix approach, the expression form of consensus criterion for multiple networks is simplified. Available information could be fully utilized, and the advantages of self-triggered scheme are retained. A numerical example of multiple unmanned aerial vehicles is offered to show effectiveness.

Network-based global H∞ pinning synchronisation for unmanned marine vehicles subject to disturbances

The network-based global H∞ pinning synchronisation of unmanned marine vehicles (UMVs) via sampled-data communications is investigated in this paper. By using Lyapunov stability theory, linear matrix inequality (LMI) technique and free-weighting matrix approach, some sufficient conditions are derived to ensure the global pinning synchronisation of UMVs. Furthermore, the maximum allowable sampling interval is estimated by a simple algorithm. Further study is then extended to address the global H∞ pinning synchronisation problem of UMVs with external disturbances, showing that a better H∞ performance can be guaranteed under some suitable conditions. Two numerical examples are presented to verify the validity and effectiveness of the obtained approaches.

Network-based global H∞ pinning synchronisation for unmanned marine vehicles subject to disturbances

The network-based global H∞ pinning synchronisation of unmanned marine vehicles (UMVs) via sampled-data communications is investigated in this paper. By using Lyapunov stability theory, linear matrix inequality (LMI) technique and free-weighting matrix approach, some sufficient conditions are derived to ensure the global pinning synchronisation of UMVs. Furthermore, the maximum allowable sampling interval is estimated by a simple algorithm. Further study is then extended to address the global H∞ pinning synchronisation problem of UMVs with external disturbances, showing that a better H∞ performance can be guaranteed under some suitable conditions. Two numerical examples are presented to verify the validity and effectiveness of the obtained approaches.

Resilient Control Design Based on a Sampled-Data Model for a Class of Networked Control Systems Under Denial-of-Service Attacks.

This article is concerned with designing resilient state feedback controllers for a class of networked control systems under denial-of-service (DoS) attacks. The sensor samples system states periodically. The DoS attacks usually prevent those sampled signals from being transmitted through a communication network. A logic processor embedded in the controller is introduced to not only receive sampled signals but also capture information on the duration time of each DoS attack. Note that the duration time of DoS attacks is usually both lower and upper bounded. Then the closed-loop system is modeled as an aperiodic sampled-data system closely related to both lower and upper bounds of duration time of DoS attacks. By introducing a novel looped functional, which caters for the N -order canonical Bessel-Legendre inequalities, some N -dependent stability criteria are presented for the resultant closed-loop system. It is worth pointing out that a number of identity formulas are uncovered, which enable us to apply the notable free-weighting matrix approach to derive less conservative stability criteria. A linear-matrix-inequality-based criterion is provided to design stabilizing state-feedback controllers against DoS attacks. A satellite control system is given to demonstrate the effectiveness of the proposed method.

Finite-time Stability, Dissipativity and Passivity Analysis of Discrete-time Neural Networks Time-varying Delays

The neural network time-varying delay was described as the dynamic properties of a neural cell, including neural functional and neural delay differential equations. The differential expression explains the derivative term of current and past state. The objective of this paper obtained the neural network time-varying delay. A delay-dependent condition is provided to ensure the considered discrete-time neural networks with time-varying delays to be finite-time stability, dissipativity, and passivity. This paper using a new Lyapunov-Krasovskii functional as well as the free-weighting matrix approach and a linear matrix inequality analysis (LMI) technique constructing to a novel sufficient criterion on finite-time stability, dissipativity, and passivity of the discrete-time neural networks with time-varying delays for improving. We propose sufficient conditions for discrete-time neural networks with time-varying delays. An effective LMI approach derives by base the appropriate type of Lyapunov functional. Finally, we present the effectiveness of novel criteria of finite-time stability, dissipativity, and passivity condition of discrete-time neural networks with time-varying delays in the form of linear matrix inequality (LMI).

Finite-Time Synchronization of Input Delay Complex Networks via Non-fragile Controller

This paper investigates the finite-time synchronization problem of complex networks subject to input delay. The time-varying sampling is required to be aperiodic, which implies that the difference of any two continuous sampling instants does not exceed a given upper bound. Together with free-weighting matrix approach, a fresh Lyapunov functional is employed to establish a sufficient condition, solving the finite-time synchronization problem. Then, the synchronization of complex networks with input time-varying delay within a given time interval is considered. In order to solve such a problem, sufficient conditions are obtained based on non-fragile control protocol, the Lyapunov-Krasovskii stability theory (LKST) and integral inequality. The finite-time stability of complex networks in the presence of delay input delay can be achieved. At last, the smaller conservatism and the effectiveness of the obtain theoretical result is exhibited through some numerical simulations.