LMI-based Criterion Research Articles

H∞ observer-based controller synthesis for fractional order systems over finite frequency range

This paper focuses on the H∞ observer-based control problem for fractional order systems (FOSs) over finite frequency range. Firstly, as an extension to the KYP lemma, the structure singular value–μ and its upper bound are analyzed and determined. The necessary and sufficient conditions of the H∞ performance for FOSs over finite frequency range are given through the generalized μ analysis method. This method is different from the traditional μ-analysis method, which is only suitable for integer order systems. Secondly, according to these obtained LMI-based criteria for H∞ performance index and a key projection lemma, we design an H∞ observer-based controller to stabilize the estimation error and decrease the H∞ norm for the FOS simultaneously. With the help of the matrix congruence transformation, the feedback gain matrix is parameterized by a scalar matrix. Thirdly, to deal with the nonlinear terms in matrix inequalities, an iterative linear matrix inequality (ILMI) algorithm is developed. Finally, two numerical examples are provided to explain the correctness of the established results.

Impulsive Control and Synchronization for Fractional-Order Hyper-Chaotic Financial System

This paper reports a new global Mittag-Leffler synchronization criterion with regard to fractional-order hyper-chaotic financial systems by designing the suitable impulsive control and the state feedback controller. The significance of this impulsive synchronization lies in the fact that the backward economic system can synchronize asymptotically with the advanced economic system under effective impulse macroeconomic management means. Matlab’s LMI toolbox is utilized to deduce the feasible solution in a numerical example, which shows the effectiveness of the proposed methods. It is worth mentioning that the LMI-based criterion usually requires the activation function of the system to be Lipschitz, but the activation function in this paper is fixed and truly nonlinear, which cannot be assumed to be Lipschitz continuous. This is another mathematical difficulty overcome in this paper.

LMI-based criterion for global Mittag-Leffler lag quasi-synchronization of fractional-order memristor-based neural networks via linear feedback pinning control

This paper addresses global Mittag-Leffler lag quasi-synchronization (GMLQS) of fractional-order memristor-based neural networks (FMNNs). Firstly, for a general class of fractional-order nonlinear systems with interval uncertainties, a kind of linear feedback pinning controller, which works by feeding back partial state errors to the partial controlled variables, is designed to achieve global Mittag-Leffler ultimate boundedness (GMUB). Correspondingly, a GMUB criterion in the form of linear matrix inequality (LMI) is derived with the aid of a Lyapunov function and a newly established fractional-order differential inequality. Then, the linear feedback pinning controller is employed for GMUB of the synchronization error system, which is equivalent to GMLQS of FMNNs. Since there exists the propagation delay between drive-response FMNNs and the synchronization error system can not be obtained straightforwardly, an identical equation about Caputo’s fractional derivatives is established to overcome this difficulty. Moreover, the detailed pinning control scheme design procedures for a prescribed GMLQS performance are presented, where the performance involves both ultimate error bound and transient behavior. In the control scheme, an auxiliary LMI and an optimization objective function are introduced, which can significantly reduce control cost. Finally, a numerical example is presented to show the feasibility of the control scheme. The results obtained in this paper have improved the existing criterion on quasi-synchronization of FMNNs, and will also provide a novel insight into pinning control of fractional-order nonlinear systems.

LMI-based criterion on stochastic ISS property of delayed high-order neural networks with explicit gain functions and simply event-triggered mechanism

In this paper, by transforming the high-order system into the system with vector-matrix form, the authors employed variational methods in Sobolev spaces, Lyapunov function method, Dynkin’s formula and comparison principle to deduce the stochastic input-to-state stability in mean square on the high-order time-delays reaction-diffusion neural networks under the concise event-triggered mechanism. Remarkably, it is the first paper in which the LMI-based criterion of input-to-state stability of time-delays high-order reaction-diffusion neural networks with event-triggered control is derived, in which the diffusion item plays its role. Not similarly as those of previous literature, the sufficient conditions of the main result in this paper are not involved to Lyapunov function, which implies that the conditions of this paper is easier to be verified than ever. With the help of computer Matlab LMI toolbox, a numerical example illustrates the effectiveness of proposed methods.

Robust mixed performance of uncertain switched systems with random time-varying delay

ABSTRACTIn this paper, the robust mixed / performance analysis of uncertain switched systems with linear fractional perturbations and random time-varying delay via a switching signal selection is considered. Some delay-dependent LMI-based criteria are proposed to achieve the design of switching signal. Our approach is proposed to guarantee the performance of system under consideration by Wirtinger-based inequality. Finally, two numerical examples are illustrated to show the main results.

Necessary Conditions for Complete Synchronization of a Coupled Chaotic Aihara Neuron Network with Electrical Synapses

In this paper, the synchronization problem of a chaotic Aihara neuron network is considered. Based on the master stability function (MSF) analysis, some necessary conditions are proposed to investigate the complete synchronization of the electrical coupled chaotic Aihara neuron networks. Especially, the two-dimensional parameter-space plots are obtained numerically to visualize the possible synchronized region. For the chaotic Rulkov neuron network, the numerical simulations of the MSF show that complete synchronization of the electrical coupled Aihara neuron network can be achieved when the coupling strength lies in a suitable interval, while it is highly improbable to attain complete synchronization when all neurons are in the chaotic bursting. Moreover, the complete synchronization cannot be reached with further increase or decrease of coupling strength. These results are probably common features as far as discrete-time neuron networks are concerned. Finally, based on the drive-response active control method, an LMI-based criterion is obtained to ensure complete synchronization of the available chaotic Aihara neuron network. The spatiotemporal patterns measured by the state distribution of neurons are employed to validate the effectiveness of our control scheme.

System Computing and Simulation for Big Data Dissonances: A LMI-based Criterion for Fuzzy Large-Scale Systems

System Computing and Simulation for Big Data Dissonances: A LMI-based Criterion for Fuzzy Large-Scale Systems

Synthesized AI LMI-based Criterion for Mechanical Systems

Synthesized AI LMI-based Criterion for Mechanical Systems

Simple switching signal design for [formula omitted] performance and control of switched time-delay systems

In this paper, a simple switching signal design scheme for H∞ performance analysis and control of switched time-delay systems with linear fractional perturbations is developed. Delay-dependent LMI-based criteria are proposed to achieve the design of switching signal and control. All the LMI problems in our main results can be solved numerically by Matlab LMI toolbox. Wirtinger-based inequality is used in our approach to improve the conservativeness of the past research results. Finally, some numerical examples are illustrated to show the main improvement.

LMI-Based Criteria of Controllability and Observability for a Descriptor MIMO System

This paper develops simple LMI-based criteria of controllability and observability for a linear time-invariant descriptor (differential-algebraic) multiple-input multiple-output (MIMO) system. Several examples illustrate the efficiency of the developed criteria. A restriction of these criteria is that the number of inputs (outputs, respectively) must not be smaller than half the states of the space dimension.

Delay-independent stability criteria for complex-valued BAM neutral-type neural networks with time delays

This paper focuses on the global asymptotic stability of complex-valued bidirectional associative memory (BAM) neutral-type neural networks with time delays. By virtue of homeomorphism theory, inequality techniques and Lyapunov functional, a set of delay-independent sufficient conditions is established for assuring the existence, uniqueness and global asymptotic stability of an equilibrium point of the considered complex-valued BAM neutral-type neural network model. The assumption on boundedness of the activation functions is not required, and the LMI-based criteria are easy to be checked and executed in practice. Finally, we give one example with simulation to show the applicability and effectiveness of our main results.

Contraction Mapping Theory and Approach to LMI-Based Stability Criteria of T-S Fuzzy Impulsive Time-Delays Integrodifferential Equations

In this paper, Banach fixed point theorem is employed to derive LMI-based exponential stability of impulsive Takagi-Sugeno (T-S) fuzzy integrodifferential equations, originated from Cohen-Grossberg Neural Networks (CGNNs). As far as we know, Banach fixed point theorem is rarely employed to derive LMI criteria for T-S fuzzy CGNNs, and this inspires our present work. It is worth mentioning that the conditions on the behavior functions are weaker than those of existing results, and the formulated contraction mapping and fixed point technique are different from those of previous literature. Even a corollary of our main result improves one of existing main results due to extending linear function to nonlinear function. Besides, the LMI-based criteria are programmable for computer MATLAB LMI toolbox. Moreover, an analytical table and a numerical example are presented to illustrate the advantage, feasibility, and effectiveness of the proposed methods.

Fixed Points and Exponential Stability for Impulsive Time-Delays BAM Neural Networks via LMI Approach and Contraction Mapping Principle

The fixed point technique has been employed in the stability analysis of time-delays bidirectional associative memory (BAM) neural networks with impulse. By formulating a contraction mapping in a product space, a new LMI-based exponential stability criterion was derived. Lately, fixed point methods have educed various good results inspiring this work, but those criteria cannot be programmed by a computer. In this paper, LMI conditions of the obtained result can be applicable to computer Matlab LMI toolbox which meets the need of the large-scale calculation in real engineering. Moreover, a numerical example and a comparable table are presented to illustrate the effectiveness of the proposed methods.

Improved robust exponential stability for Takagi–Sugeno fuzzy uncertain systems with time-varying delays

This paper concerns managing the robust exponential stability problem of uncertain Takagi–Sugeno fuzzy systems with time-varying delay by employing a further improved integral inequality matrix approach. Based on the linear matrix inequality (LMI) approach, delay-dependent robust exponential stability criteria have been developed. By taking the relationship among the time-varying delay, its upper bound and their difference into account, some less conservative LMI-based delay-dependent robust exponential stability criteria are obtained without ignoring any useful terms in the derivative of Lyapunov–Krasovskii functionals. Maximum allowable upper bound for time-varying delays is determined. Numerical examples are provided to show that the obtained results significantly improve the allowed upper bounds of delay size over some methods existing in the literature.

Robust stability analysis for discrete and distributed time-delays Markovian jumping reaction-diffusion integro-differential equations with uncertain parameters

In this paper, the authors employ Lyapunov stability theory, and the M-matrix, H-matrix, and linear matrix inequality (LMI) techniques and variational methods to obtain the LMI-based stochastically exponential robust stability criterion for discrete and distributed time-delays Markovian jumping reaction-diffusion integro-differential equations with uncertain parameters, whose background of physics and engineering is bidirecional associative memory (BAM) neural networks. It is worth mentioning that an LMI-based stability criterion can easily be computed by the Matlab toolbox which has high efficiency and other advantages in large-scale engineering calculations. Since using the M-matrix and H-matrix methods is not easy in obtaining the LMI criterion conditions, the methods employed in this paper improve those of previous related literature to some extent. Moreover, a numerical example is presented to illustrate the effectiveness of the proposed methods.

LMI-Based Stability Criterion for Impulsive Delays Markovian Jumping Time-Delays Reaction-Diffusion BAM Neural Networks via Gronwall-Bellman-Type Impulsive Integral Inequality

Lyapunov stability theory, variational methods, Gronwall-Bellman-type inequalities theorem, and linear matrices inequality (LMI) technique are synthetically employed to obtain the LMI-based global stochastic exponential stability criterion for a class of time-delays Laplace diffusion stochastic equations with large impulsive range under Dirichlet boundary value, whose backgrounds of physics and engineering are the impulsive Markovian jumping time-delays reaction-diffusion BAM neural networks. As far as the authors know, it is the first time to derive the LMI-based criterion by way of Gronwall-Bellman-type inequalities, which can be easily and efficiently computed by computer Matlab LMI toolbox. And the obtained criterion improves the allowable upper bounds of impulse against those of some previous related literature. Moreover, a numerical example is presented to illustrate the effectiveness of the proposed methods.

Robust Stability Analysis for T-S Fuzzy Neural Networks with Time-varying Delays

In this paper, the robust stability of T-S fuzzy uncertain system for neural networks with time-varying delays is investigated. The constraint on the time-varying delay function is removed, which means that a fast time-varying delay is allowed. Based on the Lyapunov- Krasovskii functional techniques and integral inequality approach (IIA), novel robust stability criteria have been derived in terms of linear matrix inequalities which can be easily solved using the efficient convex optimization algorithm. By taking the relationship among the time-varying delay, its upper bound and their difference into account, some less conservative LMI-based delay-dependent stability criteria are obtained without ignoring any useful terms in the derivative of Lyapunov-Krasovskii functional. Examples are included to illustrate our results. These results are shown to be less conservative than those reported in the literature.

A note on the improved LMI-based criterion for global asymptotic stability of 2-D state-space digital filters described by Roesser model using twoʼs complement overflow arithmetic

This paper focuses on some critical issues in a recently reported approach [V. Singh, Improved LMI-based criterion for global asymptotic stability of 2-D state-space digital filters described by Roesser model using twoʼs complement overflow arithmetic, Digital Signal Process. 22 (2012) 471–475] for the global asymptotic stability of two-dimensional (2-D) fixed-point state-space digital filters described by the Roesser model employing twoʼs complement overflow arithmetic. In particular, it is highlighted that the situation where Singhʼs approach can be applied to ensure the global asymptotic stability of digital filters in the presence of twoʼs complement overflow nonlinearities is not conceivable. • We focus on critical issues in a recent approach for stability of 2-D digital filter. • It is hard to conceive any situation where the reported approach can be applied. • Implication of the approach in the context of 1-D digital filter is discussed.

LMI-Based Stability Criteria for Discrete-Time Lur'e Systems With Monotonic, Sector- and Slope-Restricted Nonlinearities

This note presents new LMI-based stability criteria for the discrete-time multivariable Lur'e system with nonlinearities that are monotonic, sector- and slope-restricted. Corresponding Lur'e-Lyapunov functions are constructed for such a system. The new criteria are expressed in a reasonably general form that can be applied to both non-diagonal and diagonal nonlinearities. We explicitly compare the new approach to the existing LMI-based Popov-like criteria in the literature, and express the results in terms of an Integral Quadratic Constraint (IQC). The applications of the new criteria to some control problems and strategies are briefly discussed. Numerical examples are included to show their performance, and they are shown to be less conservative than the previous results.

LMI-Based Stability Criterion of Impulsive T-S Fuzzy Dynamic Equations via Fixed Point Theory

By formulating a contraction mapping and the matrix exponential function, the authors apply linear matrix inequality (LMI) technique to investigate and obtain the LMI-based stability criterion of a class of time-delay Takagi-Sugeno (T-S) fuzzy differential equations. To the best of our knowledge, it is the first time to obtain the LMI-based stability criterion derived by a fixed point theory. It is worth mentioning that LMI methods have high efficiency and other advantages in largescale engineering calculations. And the feasibility of LMI-based stability criterion can efficiently be computed and confirmed by computer Matlab LMI toolbox. At the end of this paper, a numerical example is presented to illustrate the effectiveness of the proposed methods.