Augmented Lyapunov Research Articles

New results on stabilization analysis for fuzzy semi-Markov jump chaotic systems with state quantized sampled-data controller

This paper, by designing a state quantized sampled-data controller, studies the issue of stochastic stabilization for fuzzy chaotic semi-Markov jump systems (FCSMJSs). First of all, to fully utilize more inner sampling information, a newly augmented Lyapunov functional is constructed on the basis of the proposed sampling-instant-to-present-time fragmentation (SITPTF) approach. Next, a new zero-valued equation, which increases the combinations of some resulting vectors, is given for the first time. After that, a useful discontinuous Lyapunov functional (DLF), which takes full advantage of the property of Wirtinger inequality, is proposed for the FCSMJSs with state quantized sampled-data controller. With the novel augmented Lyapunov functional, the DLF and new zero-valued equation, stochastic stabilization conditions are established. Moreover, in the case of no semi-Markov jump, new stabilization criteria are also got. Compared with some previous criteria, the novel stabilization criteria show less conservatism. Finally, the effectiveness and advantages of the proposed results are shown by several numerical examples.

Robust H∞ controller design for uncertain 2D continuous systems with interval time-varying delays

ABSTRACTThe design of delay-dependent robust controllers is solved here for a class of uncertain 2D continuous systems: those with interval time-varying delays and norm-bounded parameter uncertainties. By constructing a novel augmented Lyapunov–Krasovskii functional and then using the Wirtinger inequality, a new delay-dependent stability condition is developed, that uses the known lower and upper bounds of the time-varying delays to develop less conservative solutions that previous results in the literature. This condition is then applied to performance analysis and robust controller design, using linear matrix inequalities (LMIs). Two numerical examples are presented that illustrate the effectiveness of the proposed method.

Stability analysis and stabilisation of delayed IT2 fuzzy systems based on the Bessel–Legendre inequality

This study is concerned with the problems of asymptotic stability analysis and stabilisation for interval type-2 (IT2) fuzzy systems with time-varying delays. An augmented Lyapunov–Krasovskii functional including triple-integral terms is constructed. By the second-order Bessel–Legendre integral inequality and the reciprocally convex combination, a good estimation of the derivative for the Lyapunov–Krasovskii functional can be derived. Thus, sufficient asymptotic stability conditions for the delayed IT2 fuzzy system are established. The proposed method provides improvements and produces better results than the existing ones in the literature. Furthermore, in light of Finsler's lemma and the obtained asymptotic stability conditions, a state feedback controller for the delayed IT2 fuzzy system is developed. Finally, three numerical examples are given to illustrate the effectiveness of the proposed results.

Dissipativity Analysis for Neural Networks With Time-Varying Delays Based on Augmented Second-Order Delay-Product-Type Functionals

This paper investigates the problem of dissipativity of a class of neural networks with timevarying delays. First, a suitable augmented Lyapunov functional containing the second-order delay-product term is constructed. Based on the integral inequality method and the recently developed relaxed quadratic function negative-determination lemma, a strictly (Q, S, Z)-γ-dissipative criterion is derived in forms of linear matrix inequality (LMI). Finally, a numerical example is used to verify the advantages of the proposed method.

Wireless sensor network model with uncertain delay and packet loss based on intelligent fuzzy system

The utilization of fuzzy logic in WSNs is demonstrated to be a promising procedure since it permits joining and assessing various parameters in an effective way. Fuzzy logic is a decent methodology because of the execution prerequisites can be effectively supported by sensor hubs, while it can improve the general system execution. This paper studies the robust H∞ control considering time delay and packet loss related uncertainty in wireless sensor network system based on the basic theory of intelligent fuzzy systems. The model of a wireless sensor network with questionable time lag and packet loss is given first. The stability of the system is proved by the augmented Lyapunov functional and the linear matrix inequality (LMIs) method, with its demonstrated H∞ property. In order to solve the uncertain time delay and packet loss, the memory robust H∞ controller is proposed based on LMIs. Numerical examples and simulation results examines the potency of the presented method in solving the delay and packet loss of wireless sensor networks as well as the accuracy and precision of the system.

Global Exponential Stability of Delayed Neural Networks Based on a New Integral Inequality

This paper focuses on the problem of exponential stability for a class of neural networks with time-varying delays. A more general inequality is established which extends the auxiliary function-based integral inequality. Based on the inequality and parameter-dependent matrix inequality, an improved delay-dependent stability criterion is obtained by constructing an augmented Lyapunov functional. Three numerical examples are given to illustrate the efficiency of the method.

On criteria for stability of uncertain Lur’e systems of neutral type

Robust stability of uncertain Lur’e systems of neutral type is investigated in this brief. By constructing an augmented Lyapunov–Krasovskii functional, employing a new integral inequality, and Finsler lemma, less conservatism delay-dependent stability conditions for the system are established. The main contribution of the current work is to get the larger delay bounds than the existing ones in the literature in forms of linear matrix inequalities. Lastly, two typical models in this field are given and used for comparison with other remarkable results to test the efficiency of the proposed stability conditions.

Event-based fault-tolerant control for networked control systems applied to aircraft engine system

This paper studies the observer-based fault-tolerant control (FTC) for a class of networked control systems (NCSs) subject to system fault and external disturbance. Firstly, in order to reduce the number of sampled data transmissions, an improved adaptive event-triggered mechanism (AETM) is proposed, which can not only reflect the whole real-time information of the addressed NCSs, but also help to enlarge the application areas. Then based on the triggered output signals, a combined observer is proposed to estimate the state and system fault, and the estimations are further utilized to design the fault-tolerant controller. By choosing an augmented Lyapunov–Kroasovskii functional (LKF), two sufficient conditions on co-designing the AETM, observer, and controller are presented in terms of linear matrix inequalities (LMIs). Moreover, we adopt the derived methods to tackle the robust FTC for networked aircraft engine model. Finally, two numerical examples are provided to demonstrate the effectiveness of our obtained results by some simulations and comparisons.

Static anti-windup compensator for nonlinear systems with both state and input time-varying delays

In this work, the design on static anti-windup compensator (SAWC) for a class of nonlinear systems with saturation constraint is presented, in which both state time-varying delay and input one are involved. First, by utilizing an augmented Lyapunov–Krasovskii functional (LKF), sector condition, and L2 gain reduction for exogenous input, a sufficient condition on local stability is presented in terms of linear matrix inequalities (LMIs), which is later extended to the global stability issue. During the discussions, an improved dynamical Lyapunov method is initially proposed and it can fully utilize the individual and mutual information on both state and input delays. Especially, some effective techniques are utilized to given more tighter estimations on the LKF’s derivatives. In all, these treatments above can result in much less conservatism. Finally, some comparisons and simulations are presented in two numerical examples under the proposed SAWC.

Robust $H_{\infty }$ Control for T–S Fuzzy Systems With State and Input Time-Varying Delays via Delay-Product-Type Functional Method

This paper investigates the problem of robust $H_{\infty }$ control for a class of nonlinear systems with state and input time-varying delays. The nonlinearity is presented by a continuous-time Takagi-Sugeno (T-S) fuzzy model with parameter uncertainties. A sufficient asymptotic stability condition is first proposed by constructing a delay-product-type augmented Lyapunov–Krasovskii functional and utilizing an extended reciprocally convex matrix inequality together with a Wirtinger-based integral inequality. Then, a state feedback controller is derived that guarantees the closed-loop fuzzy system being asymptotically stable with an $H_{\infty }$ performance index. Finally, four numerical examples are given to reveal the effectiveness and merits of the developed new design techniques.

M91 INCREASED SCHIZOPHRENIA FAMILY HISTORY BURDEN AND REDUCED PREMORBID IQ IN TREATMENT-RESISTANT SCHIZOPHRENIA: A SWEDISH NATIONAL REGISTER AND GENOMIC STUDY

This paper is concerned with the stability analysis of time-varying delay neural networks. By introducing some new delay integral terms and relaxation matrix, an augmented Lyapunov–Krasovskii functional (LKF) is constructed. In dealing with the inequality relations, a new method is proposed to deal with the integral term, which makes the inequality contain more neural network information and delay information. By solving the convergence of inequalities, the conservatism of the stability condition is improved and a more larger admissible maximum upper bounds (AMUBs) is obtained. Finally, some numerical examples are given to prove the effectiveness of the proposed method.

Robust delay-dependent H∞ filtering for uncertain Takagi–Sugeno fuzzy neutral stochastic time-delay systems

This paper addresses the robust H∞ filter design problem for a class of uncertain fuzzy neutral stochastic system with time-delay through Takagi–Sugeno (T–S) fuzzy model. By constructing an augmented Lyapunov–Krasovskii functional, some novel delay-dependent stability criteria for uncertain fuzzy neutral stochastic system with time varying delay are obtained in terms of linear matrix inequalities. By using the integral inequality in the neutral stochastic setting combined with delay decomposition approach, the H∞ fuzzy filter is designed to guarantee the corresponding filtering error systems robustly asymptotically stable with a specified H∞ performance index. At last, two numerical examples are presented to show the less conservatism than the previous results.

Delay-Dependent Stability Analysis of Multi-Area Load Frequency Control With Enhanced Accuracy and Computation Efficiency

This paper aims at improving calculation accuracy and reducing calculation burden of delay-dependent stability analysis for large-scale multi-area load frequency control (LFC) schemes in traditional and deregulated environments. The special features of the LFC models have been exploited via model reconstruction technique to equivalently transform the original LFC model into a delay-free part and a delay-related part by a transition matrix. The improvement of the calculation efficiency is obtained by decreasing both the number of decision variables and the maximal order of the linear matrix inequalities. Based on the reconstructed model, a novel augmented Lyapunov functional is constructed mainly based on the delay-related part with much lower order and its derivative is bounded with the Wirtinger inequality to establish a stability condition with less conservatism. Case studies are based on two-area LFC systems to verify the effectiveness of proposed stability criteria based on the time-domain indirect method, with a great improvement of the calculation accuracy that can achieve almost accurate delay margins, such as the frequency domain method. Moreover, comparing with the criterion based on the original system model without reconstruction, the calculation efficiency has been greatly improved with the cost of small deduction of accuracy.

Finite-time boundedness of state estimation for semi-Markovian jump systems with distributed leakage delay and linear fractional uncertainties

ABSTRACTIn this paper, the problem of finite-time bounded control for uncertain semi-Markovian jump neural networks with mixed delays which include distributed leakage delay (DLD) and mixed time-varying delays is considered. The system not only contains semi-Markovian jump, linear fractional uncertainties (LFUs), mixed time-varying delays but also includes distributed time delays in the leakage term which is not yet investigated in existing papers. Firstly, uncertainty parameters in the systems are solved by LFU based on the new model. Secondly, a novel augmented Lyapunov–Krasovskii functional (LKF) which involves more information about time-varying delays is constructed. Moreover, latest integral inequalities and time-delays division method are used to estimate the derivative of proposed LKFs. Thirdly, in the framework of uncertainty, semi-Markovian jump, DLD, mixed delays and external disturbance, a full-order state estimator is constructed such that the error dynamic system is finite-time bounded under the condition of given linear matrix inequalities. Finally, usefulness and advantages of the obtained results are verified by three numerical examples.

Robust Output Feedback Stabilization for Uncertain Discrete-Time Stochastic Neural Networks with Time-Varying Delay

This paper investigates the problem of robust exponential stabilization of uncertain discrete-time stochastic neural networks with time-varying delay based on output feedback control. By choosing an augmented Lyapunov–Krasovskii functional, we established the sufficient conditions of the delay-dependent asymptotical stabilization in the mean square for a class of discrete-time stochastic neural networks with time-varying delay. Furthermore, we obtain the criteria of robust global exponential stabilization in the mean square for uncertain discrete-time stochastic neural networks with time-varying delay. Finally, we give numerical examples to illustrate the effectiveness of the proposed results.

New results on stability analysis of systems with time-varying delays using a generalized free-matrix-based inequality

This paper addresses the delay-dependent stability problem of linear systems with interval time-varying delays. A generalized free-matrix-based inequality is proposed and employed to derive stability conditions, which are less conservative than the Bessel–Legendre inequality. An augmented Lyapunov–Krasovskii functional is tailored for the generalized free-matrix-based inequality. Then, some items in the Lyapunov–Krasovskii functionals are integrated so as to relax its positive definite condition, which provides a more accurate lower bound for the Lyapunov–Krasovskii functionals. Therefore, some less conservative stability criteria are presented. Two numerical examples illustrate the effectiveness of the method.

An Improved Approach to Robust $$H_\infty $$ Filtering for Uncertain Discrete-Time Systems with Multiple Delays

This paper is concerned with the robust $$H_\infty $$ filtering problem for a class of discrete-time systems with polytopic uncertainties and multiple time delays. Different from the most existing techniques, the novel augmented Lyapunov–Krasovskii functionals are constructed by incorporating the relationships between multiple time delays. Based on the proposed functionals and the Wirtinger-based inequality, sufficient conditions are first established under which the filtering error system is asymptotically stable and has an prescribed $$H_\infty $$ performance level. Then, the adjusting parameters are introduced such that the filter gains can be effectively obtained by solving certain linear matrix inequalities. Finally, two numerical examples are given to demonstrate the effectiveness and the benefit of the proposed approach.

Improved LMI-based stability conditions for a competitive Lotka\u2013Volterra system with time-varying delays

This paper is concerned with the local asymptotic stability problem for a competitive Lotka–Volterra system with time-varying delays. By constructing the novel augmented Lyapunov–Krasovskii functionals and using the Wirtinger integral inequality, some alternative stability criteria are obtained by means of linear matrix inequalities. In particular, our constructed functionals contain some cross terms related to four different time delays. The proposed stability conditions in this paper are less conservative as compared with the most existing ones due to using some advanced techniques. Finally, a numerical example illustrates the effectiveness and improvement of the obtained results.

State estimation for neural networks with two additive time-varying delay components using delay-product-type augmented Lyapunov–Krasovskii functionals

This paper focuses on the state estimation issue of neural networks with two additive time-varying delay components. By constructing a suitable augmented Lyapunov–Krasovskii functional, more time delay information is considered. Using the recently developed reciprocally convex inequality, some reciprocally convex combinations can be estimated more closely. The design conditions of state estimators are expressed as linear matrix inequalities (LMIs). The delay-product-type Lyapunov–Krasovskii functional is used to further reduce the conservativeness. With the help of state estimation method, the stability conditions of neural networks with two additive time-varying delay components are also developed. Finally, two numerical examples widely used in the literature show the effectiveness of the proposed method.

Stability analysis of systems with time-varying delay via novel augmented Lyapunov–Krasovskii functionals and an improved integral inequality

Delay-dependent stability analysis of linear systems with a time-varying delay is investigated in this paper. Firstly, instead of developing a Lyapunov–Krasovskii functional (LKF) including augmented non-integral quadratic terms as usual, this paper proposes two augmented-integral-function based LKFs, which can reflect closer relationships among system states. Secondly, to bound the derivative of LKF more accurately, a new integral inequality with several free matrices is developed. Compared with the free-matrix-based integral inequality, this inequality can provide additional freedom due to the free matrices introduced. Then, by employing those LKFs and the improved integral inequality, several delay-dependent stability criteria are established for two types of delays. Finally, two numerical examples are given to demonstrate the superiority of the proposed method.