Feisheng Yang

Stability Analysis for Neural Networks With Time-Varying Delay Based on Quadratic Convex Combination

This paper studies the problem of stability analysis for neural networks (NNs) with a time-varying delay. The activation functions are assumed to be neither monotonic, nor differentiable, nor bounded. By defining a more general type of Lyapunov functionals, some new less conservative delay-dependent stability criteria are obtained and shown in terms of linear matrix inequalities (LMIs). Since less variables are involved, the computational complexity of the new conditions is reduced. Numerical examples are given to illustrate the effectiveness and the benefits of the proposed method.

Mode-independent fuzzy fault-tolerant variable sampling stabilization of nonlinear networked systems with both time-varying and random delays

This paper develops a fault-tolerant variable sampling control (VSC) scheme for a class of nonlinear networked control systems (NCSs) with time-varying state and random network delays. An uncertain continuous Takagi-Sugeno (T-S) fuzzy system with both state and input varying delays, in the presence of possible actuator faults, is obtained equivalently on the basis of the input delay methodology. A tighter bounding lemma is proposed so as to gain less conservative closed-loop stability criteria. Delay-dependent conditions in terms of linear matrix inequalities are derived for the mode-independent fault-tolerant stabilizing controller of the resulting Markovian network-based system by employing a novel stochastic Lyapunov-Krasovskii (L-K) functional. An illustrative example is simulated to show the validity of the obtained results.

T-S Model-based Relaxed Reliable Stabilization of Networked Control Systems with Time-varying Delays under Variable Sampling

This paper investigates the reliable stabilization problem for a class of nonlinear networked control systems (NCSs) under variable sampling with variant state and network delays. An equivalent continuous-time uncertain fuzzy system with both state and input time varying delays, subject to possible actuator faults, is derived based on the Takagi-Sugeno (T-S) model and the input delay method. In order to obtain much less conservative results for the delay system transformed, a more relaxed stabilizability condition of a delay-free T-S system and a tighter bounding lemma for some derivative terms of the constructed functional are utilized for closed-loop stability determination of the NCS under variable sampling. Delay-dependent fault-tolerant stabilization conditions formulated in terms of linear matrix inequalities for the possibly faulty network-based system are derived by employing a novel Lyapunov- Krasovskii (L-K) functional, which makes good use of the information of both the lower and upper bounds on the two interval delays. An example is provided to show the validity of the obtained results.

Quadratically convex combination approach to stability of T–S fuzzy systems with time-varying delay

Abstract This paper develops a novel stability analysis method for Takagi–Sugeno (T–S) fuzzy systems with time-varying delay. New delay-dependent stability criteria in terms of linear matrix inequalities for time-varying delayed T–S fuzzy systems are derived by the newly proposed augmented Lyapunov–Krasovski (L–K) functional. This functional contains the cross terms of variables and quadratic terms multiplied by a higher degree scalar function. Different from previous results, our derivation applies the idea of second-order convex combination, and the property of quadratic convex function without resorting to the Jensens inequality. Two numerical examples are provided to verify the effectiveness of the presented results.

Delay-dependent resilient-robust stabilisation of uncertain networked control systems with variable sampling intervals

This work is concerned with the robust resilient control problem for uncertain networked control systems (NCSs) with variable sampling intervals, variant-induced delays and possible data dropouts, which is seldom considered in current literature. It is mainly based on the continuous time-varying-delay system approach. Followed by the nominal case, delay-dependent resilient robust stabilising conditions for the closed-loop NCS against controller gain variations are derived by employing a novel Lyapunov–Krasovskii functional which makes good use of the information of both lower and upper bounds on the varying input delay, and the upper bound on the variable sampling interval as well. A feasible solution of the obtained criterion formulated as linear matrix inequalities can be gotten. A tighter bounding technique is presented for acquiring the time derivative of the functional so as to utilise many more useful elements, meanwhile neither slack variable nor correlated augmented item is introduced to reduce overall computational burden. Two examples are given to show the effectiveness of the proposed method.

Simplified frequency method for stability and bifurcation of delayed neural networks in ring structure

In this paper, a novel procedure for the stability and Hopf bifurcation of delayed neural networks with ring topology and multiple time delays is proposed. This procedure mainly focuses on the distribution of roots of exponential polynomial which is necessary for analyzing the asymptotic properties of dynamic systems at an equilibrium. The purely imaginary roots (PIRs) of the exponential polynomial (which regards the delay @t as its parameter) are exactly determined by an intuitive graphic method. Moreover, the critical delay associating with those PIRs can be computed according to its periodicity. The obtained results are applied to the analysis of a general delayed neural network model (which means no restriction of number of neurons is posed on this general model). Eventually, the complete picture of stable regions and the Hopf bifurcation point in @t-parameter space is given. This work offers an exact, structured methodology for the local dynamical analysis of delayed neural networks. Some illustrative simulations based on a powerful continuation software are presented to prove the effectiveness of our theoretical analysis.

Retweet Behavior Prediction in Twitter

Retweet, as a main way to spread information in twitter, has been researched in a number of works. Recently research focuses on analyzing the factors of retweet behavior. However, the prediction on retweet behavior is a new challenge which is not well studied in the past. A basic fact is that different people are interested in different kinds of tweets, and they will retweet tweets which they are interested in. First, we collect tweets of different categories from valid account of famous news media as learning corpus. Second, in order to discover user interests, we classify user tweets into different categories by Bayes model. Finally, we measure user interests on tweets of different categories, and predict retweet behavior by interest measurement. This paper extends the previous study on retweet behavior, and we predict user retweet behavior as well as infer user interests. Experiment shows Bayes model has good performance on classifying tweets, and our algorithm achieves more precision than others.

New delay-dependent stability criteria for cohen-grossberg neural networks with multiple time-varying mixed delays

This paper investigates the globally asymptotical stability problem for a general class of Cohen-Grossberg neural networks with multiple mixed time-delays. Before proving the main theorem, a more generalized convex combination inequality is proposed. A new stability criterion for Cohen-Grossberg neural networks with multiple time-varying delays is obtained by the employed general inequality technique. Two examples are included to illustrate the effectiveness of the presented results.

Controller design for delay systems via eigenvalue assignment – on a new result in the distribution of quasi-polynomial roots

This paper considers the eigenvalue distribution of a linear time-invariant (LTI) system with time delays and its application to some controllers design for a delay plant via eigenvalue assignment. First, a new result on the root distribution for a class of quasi-polynomials is developed based on the extension of the Hermite–Biehler theorem. Then, such result is applied to proportional–integral (PI) controller parameter design for a first-order plant with time delay through pole placement. The complete region of PI gains can be obtained so that the rightmost eigenvalues in the infinite eigenspectrum of the closed-loop system with delay plant are assigned to desired positions in the complex plane. Furthermore, on the basis of the previous result, this paper also extended the PI control to the proportional–integral–derivative (PID) control. It is worth pointing out that this work aims to improve the performance of the closed-loop system on the premise of guaranteeing the stability.

Matrix quadratic convex combination for stability of linear systems with time-varying delay via new augmented Lyapunov functional

The paper addresses the delay-dependent stability problem for linear systems with time-varying delay. Novel delay-dependent stability criteria in terms of linear matrix inequalities for systems with state time-varying delay are derived by the newly proposed augmented Lyapunov-Krasovski (L-K) functional. A matrix-type quadratic convex combination approach is introduced to prove the negative definiteness of the derivative of the L-K functional along with the trajectory of the delayed system. Different from previous results by using the first order convex combination, our derivation applies the idea of second order convex combination, and the property of quadratic convex function without resorting to the Jensens inequality.