Linear Matrix Inequality Criterion Research Articles

RETRACTED: A critical review of internal wave dynamics. Part 1 – Remote sensing and in-situ observations

RETRACTED: A critical review of internal wave dynamics. Part 1 – Remote sensing and in-situ observations

Guaranteed cost synchronous control of time-varying delay cellular neural networks

This paper deals with the synchronization of time-varying delay cellular neural networks. Based on the Lyapunov stability analysis and the zoned discussion and maximax synthesis (ZDMS) method, the quadratic matrix inequality (QMI) criterion for the guaranteed cost synchronous controller is designed to synchronize the given chaotic systems. For the convenience to solve, using a generalized result of Schur complement, the criterion in the form of QMI is turned into the linear matrix inequality (LMI) form, which can be used efficiently via existing numerical convex optimization algorithms such as the interior-point algorithms for solving LMIs. The minimization of the guaranteed cost is further studied, and the corresponding LMI criterion for getting the controller is given. Finally, numerical examples are given to show the effectiveness of proposed guaranteed cost synchronous control and its corresponding minimization problem.

Number estimation of controllers for pinning a complex dynamical network

Number estimation of controllers is a fundamental question in pinning synchronization of complex networks. This paper studies the problem of controller number in synchronizing a complex network of coupled dynamical systems by means of pinning. For a complex network with a symmetric coupling matrix and full coupling between the nodes, we formulate network synchronization via pinning as a linear matrix inequality criterion, and provide a lower bound and an upper bound of the controller number for a given complex network with fixed architecture. Several numerical examples with Barabási-Albert network topologies are provided to verify our theoretical results.

GLOBAL ROBUST SYNCHRONIZATION OF A CLASS OF NONAUTONOMOUS CHAOTIC SYSTEMS WITH PARAMETER MISMATCH VIA VARIABLE SUBSTITUTION CONTROL

This paper investigates global robust synchronization of a class of nonautonomous chaotic systems with parameter mismatch under the master–slave variable substitution control. A criterion of linear matrix inequality (LMI) for the global robust synchronization is rigorously proven and the corresponding synchronization error bound is analytically estimated. The LMI criterion is then applied to the gyrostat systems, obtaining some simple and optimized algebraic criteria for global robust synchronization of the master–slave gyrostat systems with time-varying phase mismatch under single-variable substitution configurations, further verified in a numerical example.

RETRACTED: The development of autonomous low-cost biped mobile surveillance robot by intelligent bricks

RETRACTED: The development of autonomous low-cost biped mobile surveillance robot by intelligent bricks

Delay‐Dependent Stability Criteria of Uncertain Periodic Switched Recurrent Neural Networks with Time‐Varying Delays

This paper deals with the problem of delay‐dependent stability criterion of uncertain periodic switched recurrent neural networks with time‐varying delays. When uncertain discrete‐time recurrent neural network is a periodic system, it is expressed as switched neural network for the finite switching state. Based on the switched quadratic Lyapunov functional approach (SQLF) and free‐weighting matrix approach (FWM), some linear matrix inequality criteria are found to guarantee the delay‐dependent asymptotical stability of these systems. Two examples illustrate the exactness of the proposed criteria.

RETRACTED: Stability analysis of community and ecosystem hierarchies using the Lyapunov method

RETRACTED: Stability analysis of community and ecosystem hierarchies using the Lyapunov method

RETRACTED: Identification and monitoring of bridge health from ambient vibration data

Many bridges in Taiwan have been in use from the period that Taiwan was governed by the Japanese, over 50 years ago, which is the average ultimate usable lifetime of such structures. Three-quarters of the bridges on major highways have been in use for more than 20 years and numerous bridges on country roads have also been in use for more than 20 years. In other words, most of the bridges in Taiwan are aging and may require repair or replacement. Ambient vibration tests are utilized to measure the response of old bridges, which are difficult to equip with accelerometers. The Fourier transform method is traditionally used to gain important information about ambient vibration records. However, the development of information technology over the last 20 years has meant that there are more kinds of signal management technologies, including the wavelet and Hilbert—Huang transform (HHT) methods. In this study we investigate the characteristics of aging bridges by comparison with their structural properties. We analyze their ambient vibration, and discuss the possible influence of the frequency function. Long-term environmental impacts create many structural problems, but with traditional methods examination of bridge health is difficult. Therefore, in our HHT management system, we examine destroyed bridges. The characteristics and behavior of bridges subjected to random loading can be understood by analysis with the random decrement technique and the frequency response function method.

RETRACTED: A case study of damage detection in benchmark buildings using a Hilbert-Huang Transform-based method

In this study we investigate the feasibility of detecting structural damage using the Hilbert--Huang Transform (HHT) method. A damage detection index, which we call the ratio of equivalent damping ratio (RED), is proposed. The damage detection index is evaluated using the HHT and the Fast Fourier Transform (FFT) methods for the analysis of shaking table test data obtained for benchmark models based upon the Kobe and El Centro earthquakes. The results indicate that, when the response of the structure is in the elastic region, the RED value changes only slightly in both the HHT and the FFT spectra. In addition, when the structural response is nonlinear (i.e., member yielding occurs), the RED and peak ground acceleration curves indicate the incremental change in the HHT spectra. However, the same phenomena cannot be found in the FFT spectra. Moreover, there is greater change in the value of the RED for the top floor than for the other floors. Furthermore, structural damage is detected only when acceleration response data from the top floor is used. Therefore, the RED estimated from the smoothed HHT spectra is an effective and sensitive index for detecting structural damage. The proposed RED strategy will be used to establish an on-line health monitoring scheme for detecting structural damage in steel structures right after the occurrence of ground motion.

LMI criteria on exponential stability of BAM neural networks with both time-varying delays and general activation functions

Abstract In this paper, the exponential stability analysis for the bidirectional associative memory neural network model with both time-varying delays and general activation functions is considered. Neither the boundedness and the monotony on these activation functions nor the differentiability on the time-varying delays are assumed. By employing Lyapunov functional and the linear matrix inequality (LMI) approach, several new sufficient conditions in LMI form are obtained to ensure the existence, uniqueness and global exponential stability of equilibrium point for the neural networks. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The proposed stability results are less conservative than some recently known ones in the literature, which is demonstrated via an example with simulation.

RETRACTED: Fuzzy Lyapunov Stability Analysis and NN Modeling for Tension Leg Platform Systems

RETRACTED: Fuzzy Lyapunov Stability Analysis and NN Modeling for Tension Leg Platform Systems

Global synchronization criteria for a class of third-order non-autonomous chaotic systems via linear state error feedback control

This paper investigates the global synchronization of a class of third-order non-autonomous chaotic systems via the master–slave linear state error feedback control. A sufficient global synchronization criterion of linear matrix inequality (LMI) and several algebraic synchronization criteria for single-variable coupling are proven. These LMI and algebraic synchronization criteria are then applied to two classes of well-known third-order chaotic systems, the generalized Lorenz systems and the gyrostat systems, proving that the local synchronization criteria for the chaotic generalized Lorenz systems developed in the existing literature can actually be extended to describe global synchronization and obtaining some easily implemented synchronization criteria for the gyrostat systems.

RETRACTED: The Development of Half-circle Fuzzy Numbers and Application in Fuzzy Control

RETRACTED: The Development of Half-circle Fuzzy Numbers and Application in Fuzzy Control

Some improved criteria for global robust exponential stability of neural networks with time-varying delays

In this paper, some sufficient conditions for global robust exponential stability of interval neural networks with time-varying delays are presented. It is shown that our results include some counterparts of the previous literatures. On basis of the obtained results, some linear matrix inequality (LMI) criteria are derived. Moreover, three numerical examples and a simulation are given to show the effectiveness of the obtained results.

Global Asymptotic Robust Stability and Global Exponential Robust Stability of Neural Networks with Time-Varying Delays

In this paper, based on nonnegative matrix theory, the Halanay's inequality and Lyapunov functional, some novel sufficient conditions for global asymptotic robust stability and global exponential robust stability of neural networks with time-varying delays are presented. It is shown that our results improve and generalize several previous results derived in the literatures. From the obtained results, some linear matrix inequality criteria are derived. Finally, a simulation is given to show the effectiveness of the results.

Stochastic Stability of Neural Networks with Both Markovian Jump Parameters and Continuously Distributed Delays

The problem of stochastic stability is investigated for a class of neural networks with both Markovian jump parameters and continuously distributed delays. The jumping parameters are modeled as a continuous-time, finite-state Markov chain. By constructing appropriate Lyapunov-Krasovskii functionals, some novel stability conditions are obtained in terms of linear matrix inequalities (LMIs). The proposed LMI-based criteria are computationally efficient as they can be easily checked by using recently developed algorithms in solving LMIs. A numerical example is provided to show the effectiveness of the theoretical results and demonstrate the LMI criteria existed in the earlier literature fail. The results obtained in this paper improve and generalize those given in the previous literature.

Further results on state estimation for neural networks of neutral-type with time-varying delay

In this paper, further result on design problem of state estimator for a class of neural networks of neutral type is presented. A delay-dependent linear matrix inequality (LMI) criterion for existence of the estimator is derived. A numerical simulation is given to show the effectiveness of proposed estimator.

AN LMI APPROACH TO ROBUST STABILITY OF UNCERTAIN DISCRETE SINGULAR TIME-DELAY SYSTEMS

The problem of robust stability analysis for uncertain discrete singular time-delay systems is investigated in this paper. By decomposing the nominal system into slow and fast subsystems, a linear matrix inequality (LMI) condition is proposed for a discrete singular time-delay system to be regular, causal and stable. Based on this, an LMI criterion is obtained for robust stability of an uncertain discrete singular time-delay system. Two numerical examples are provided to demonstrate the feasibility of the proposed approach.

Robust stabilization for a class of nonlinear networked control systems

The problem of robust stabilization for a class of uncertain networked control systems (NCSs) with nonlinearities satisfying a given sector condition is investigated in this paper. By introducing a new model of NCSs with parameter uncertainty, network-induced delay, nonlinearity and data packet dropout in the transmission, a strict linear matrix inequality (LMI) criterion is proposed for robust stabilization of the uncertain nonlinear NCSs based on the Lyapunov stability theory. The maximum allowable transfer interval (MATI) can be derived by solving the feasibility problem of the corresponding LMI. Some numerical examples are provided to demonstrate the applicability of the proposed algorithm.

A robust observer design for chaos synchronization of uncertain systems using LMI criterion

In this paper, considering the effect of exoteric perturbation on system’s parameters, a robust observer, based on Lyapunov theory, is designed for the output synchronization of a class of uncertain systems when the full state vector is not available. With the help of LMI criterion and then using the MATLAB LMI Toolbox, the observer gain L is derived, which can not only make the outputs of both master and slave systems reach H∞ synchronization with the passage of time but also reduce the influence of the disturbance within a prescribed level. In the end, we take the perturbed Chua’s circuit as an example to illustrate that the proposed method is effective and quite robust against the effect of exoteric perturbation. Key words: Chaos synchronization, the observer method, Lyapunov theory, linear matrix inequality (LMI), PACC: 0545.