LMI Criterion Research Articles

Guaranteed cost consensus for high-dimensional multi-agent systems with time-varying delays

Guaranteed cost consensus analysis and design problems for high-dimensional multi-agent systems with timevarying delays are investigated. The idea of guaranteed cost control is introduced into consensus problems for high-dimensional multi-agent systems with time-varying delays, where a cost function is defined based on state errors among neighboring agents and control inputs of all the agents. By the state space decomposition approach and the linear matrix inequality U+0028 LMI U+0029, sufficient conditions for guaranteed cost consensus and consensualization are given. Moreover, a guaranteed cost upper bound of the cost function is determined. It should be mentioned that these LMI criteria are dependent on the change rate of time delays and the maximum time delay, the guaranteed cost upper bound is only dependent on the maximum time delay but independent of the Laplacian matrix. Finally, numerical simulations are given to demonstrate theoretical results.

Chaos Suppression of a Class of Fractional-Order Chaotic Systems with Order Lying in (1, 2)

It is shown that fractional-order (FO) nonlinear systems can also show higher nonlinearity and complex dynamics. FO chaotic systems have wider applications in secure communication, signal processing, financial field due to FO chaos has larger key space and more complex random sequences than integer-order chaos. Thanks to the lack of the effective analytical methods and controller design methods of integer-order chaotic systems can not be applied directly to FO chaos systems, to control chaos of FO chaotic systems is a very interesting and difficult problem, especially for FO chaotic system with order α:1<α<2. Based on the stability theory of FO systems and the linear state feedback control, an LMI criterion for controlling a class of fractional-order chaotic systems with fractional-order α:1<α<2 is addressed in this paper. The proposed method can be easily verified and resolved by using the Matlab LMI toolbox. Moreover, the proposed controller is linear, easy to implement and overcome some defects in the recent literature, which have improved the existing results. The method employed in this letter can effectively avoid control cost and inaccuracy in the literatures, and can be be applied to FO hyperchaos systems and synchronization controller design of FO chaotic system. Theoretical analysis and numerical simulations are presented to demonstrate the validity and feasibility of the proposed methods.

Admissible output consensualization control for singular multi-agent systems with time delays

Admissible output consensus design problems for high-order linear time-invariant singular multi-agent systems with constant time delays are dealt with. Firstly, based on the observability decomposition, a dynamic output feedback consensus protocol is proposed, which makes singular multi-agent systems satisfy some separation principle and can simplify admissible output consensus design problems. Then, LMI criteria for admissible output consensualization are presented, which can guarantee the regular and impulse-free properties of singular multi-agent systems directly. Moreover, an approach to determine the output consensus function is presented on the basis of the first equivalent form and the impacts of initial states of consensus protocols and dynamic agents are determined, respectively. Finally, numerical examples are shown to demonstrate theoretical 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.

Pinning control for synchronization of nonlinear complex dynamical network with suboptimal SDRE controllers

Based on the state-dependent Riccati equation (SDRE) technique, in this paper, a suboptimal pinning control scheme is proposed to synchronize linearly coupled complex networks. The Lyapunov direct method is used to analyze the stability of the closed-loop control system, where it leads to a LMI criterion for pinning synchronization. It is shown that the time interval for synchronization of the proposed SDRE controllers is faster comparing with the results in the latest literatures. It is also shown that the minimum required coupling weights for the network synchronization in a finite desired time is decreased when some specified nodes in the network are pinned with the SDRE controllers. Based on the proposed criterion for pinned nodes selection, the network performances for different topological structures are investigated and the results are compared. The results indicate that the coupling weights for network synchronization in finite desired time in random Erdos Reiny networks are minimum when the pinned nodes are selected based on the minimum matching theorem. In small-world and scale-free networks, the minimum required coupling weight for network synchronization in finite desired time decreases when the highest degree nodes are pinned.

Frequency-domain criterion for the chaos synchronization of time-delay power systems under linear feedback control

This paper studies the global synchronization of non-autonomous, time-delay, chaotic power systems via linear state-error feedback control. The frequency domain criterion and the LMI criterion are proposed and applied to design the coupling matrix. Some algebraic criteria via a single-variable linear coupling are derived and formulated in simple algebraic inequalities. The effectiveness of the new criteria is illustrated with numerical examples.

Augmented observer approach for high-impedance haptic system with time delay

Among others measures of performance, a haptic device may be characterized by its behavior in the implementation of a virtual wall in terms of the biggest value of the virtual stiffness leaving stable the device. This value depends on many factors including time delays and the virtual world implementation. The paper proposes a new architecture for this latter one based on the use of an augmented state observer which contributes to improve without additional costs the performance of a haptic device with respect to the standard implementation based on the use of the backward finite difference method. In order to compute the stability boundaries of the device in terms of virtual wall parameters, a new LMI criterion for the stability of discrete-time systems with time-varying delay is given. Some numerical simulation results are included to prove the effectiveness of the proposed approach.

Delay-Interval-Dependent Stability Criterion for Linear Systems With Time-Varying State Delay

This paper considers the problem of stability analysis of linear systems with a time-varying state delay. A new delay-interval-dependent stability criterion is derived without involving any direct approximation of the integral terms that involve uncertain limit of integration in the time-derivative of the Lyapunov-Krasovskii functional. This development leads to a less conservative LMI criterion as seen through numerical examples.

A novel LMI criterion for power system stability with multiple time-delays

This paper presents a novel LMI criterion for electric power system stability with multiple time-delays. Initially, the linear time-invariant model of the power system with multiple delays is constructed, subsequently, the former criteria and the novel criterion of this paper are demonstrated in this paper, and the novel criterion is fully proved according to Lyapunov direct method. Specifically, the proposed criterion utilizes a properly simplified Lyapunov-Krasovskii functional, and no free-weighting matrix is introduced in the formation of new criterion, as a consequence, the calculation efficiency is remarkably enhanced. A typical second-order delay system, a single-generator-infinite-bus system and the WSCC 3-generator-9-bus delay system are taken to validate the effectiveness and efficiency enhancement of the proposed criterion. The numerical results indicate that the criterion of this paper can generate the same stability margin with the former ones. Further, the numerical results also verify that the proposed criterion’s efficiency is substantially boosted and calculation time is greatly curtailed.

Evolved Bat Algorithm Based Adaptive Fuzzy Sliding Mode Control with LMI Criterion

Evolved Bat Algorithm Based Adaptive Fuzzy Sliding Mode Control with LMI Criterion

Evolved Bat Algorithm Based Adaptive Fuzzy Sliding Mode Control with LMI Criterion

Evolved Bat Algorithm Based Adaptive Fuzzy Sliding Mode Control with LMI Criterion

Evolved Bat Algorithm Based Adaptive Fuzzy Sliding Mode Control with LMI Criterion

Evolved Bat Algorithm Based Adaptive Fuzzy Sliding Mode Control with LMI Criterion

Evolved Bat Algorithm Based Adaptive Fuzzy Sliding Mode Control with LMI Criterion

Evolved Bat Algorithm Based Adaptive Fuzzy Sliding Mode Control with LMI Criterion

Evolved Bat Algorithm Based Adaptive Fuzzy Sliding Mode Control with LMI Criterion

Evolved Bat Algorithm Based Adaptive Fuzzy Sliding Mode Control with LMI Criterion

Evolved Bat Algorithm Based Adaptive Fuzzy Sliding Mode Control with LMI Criterion

Evolved Bat Algorithm Based Adaptive Fuzzy Sliding Mode Control with LMI Criterion

Evolved Bat Algorithm Based Adaptive Fuzzy Sliding Mode Control with LMI Criterion

Evolved Bat Algorithm Based Adaptive Fuzzy Sliding Mode Control with LMI Criterion

Evolved Bat Algorithm Based Adaptive Fuzzy Sliding Mode Control with LMI Criterion

Evolved Bat Algorithm Based Adaptive Fuzzy Sliding Mode Control with LMI Criterion

Evolved Bat Algorithm Based Adaptive Fuzzy Sliding Mode Control with LMI Criterion

Evolved Bat Algorithm Based Adaptive Fuzzy Sliding Mode Control with LMI Criterion

Luenberger-Type Observer Design for Stochastic Time-Delay Systems

This paper deals with the problem of an observer design for stochastic time-delay systems. The system states are unmeasured. We derive delay-dependent LMI criteria by means of the Leibniz-Newton formula, the Ito’s differential operator and stochastic Lyapunov stability theory in order to obtain sufficient conditions for the asymptotic stability in the mean square for the closed-loop stochastic time-delay system. The proposed conditions are easily and numerically tractable via a Matlab LMI toolbox. The effectiveness of the control strategy is verified by numerical experiments.

LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian-Jumping Cohen-Grossberg Neural Networks with Nonlinearp-Laplace Diffusion

The robust exponential stability of delayed fuzzy Markovian-jumping Cohen-Grossberg neural networks (CGNNs) with nonlinearp-Laplace diffusion is studied. Fuzzy mathematical model brings a great difficulty in setting up LMI criteria for the stability, and stochastic functional differential equations model with nonlinear diffusion makes it harder. To study the stability of fuzzy CGNNs with diffusion, we have to construct a Lyapunov-Krasovskii functional in non-matrix form. But stochastic mathematical formulae are always described in matrix forms. By way of some variational methods inW1,p(Ω),Itôformula, Dynkin formula, the semi-martingale convergence theorem, Schur Complement Theorem, and LMI technique, the LMI-based criteria on the robust exponential stability and almost sure exponential robust stability are finally obtained, the feasibility of which can efficiently be computed and confirmed by computer MatLab LMI toolbox. It is worth mentioning that even corollaries of the main results of this paper improve some recent related existing results. Moreover, some numerical examples are presented to illustrate the effectiveness and less conservatism of the proposed method due to the significant improvement in the allowable upper bounds of time delays.