Observer-based controller design of time-delay systems with an interval time-varying delay

This paper considers the problem of designing an observer-based output feedback controller to exponentially stabilize a class of linear systems with an interval time-varying delay in the state vector. The delay is assumed to vary within an interval with known lower and upper bounds. The time-varying delay is not required to be differentiable, nor should its lower bound be zero. By constructing a set of Lyapunov–Krasovskii functionals and utilizing the Newton–Leibniz formula, a delay-dependent stabilizability condition which is expressed in terms of Linear Matrix Inequalities (LMIs) is derived to ensure the closed-loop system is exponentially stable with a prescribed α-convergence rate. The design of an observerbased output feedback controller can be carried out in a systematic and computationally efficient manner via the use of an LMI-based algorithm. A numerical example is given to illustrate the design procedure.

Design of H∞ control of neural networks with time-varying delays

This paper deals with the H∞ control problem of neural networks with time-varying delays. The system under consideration is subject to time-varying delays and various activation functions. Based on constructing some suitable Lyapunov-Krasovskii functionals, we establish new sufficient conditions for H∞ control for two cases of time-varying delays: (1) the delays are differentiable and have an upper bound of the delay-derivatives and (2) the delays are bounded but not necessary to be differentiable. The derived conditions are formulated in terms of linear matrix inequalities, which allow simultaneous computation of two bounds that characterize the exponential stability rate of the solution. Numerical examples are given to illustrate the effectiveness of our results.

Observer-based control for time-varying delay neural networks with nonlinear observation

This paper studies the problem of designing observer-based controllers for a class of delayed neural networks with nonlinear observation. The system under consideration is subject to nonlinear observation and an interval time-varying delay. The nonlinear observation output is any nonlinear Lipschitzian function and the time-varying delay is not required to be differentiable nor its lower bound be zero. By constructing a set of appropriate Lyapunov-Krasovskii functionals and utilizing the Newton-Leibniz formula, some delay-dependent stabilizability conditions which are expressed in terms of Linear Matrix Inequalities (LMIs) are derived. The derived conditions allow simultaneous computation of two bounds that characterize the exponential stability rate of the closed-loop system. The unknown observer gain and the state feedback observer-based controller are directly obtained upon the feasibility of the derived LMIs stabilizability conditions. A simulation example is presented to verify the effectiveness of the proposed result.

Full-order observer design for nonlinear complex large-scale systems with unknown time-varying delayed interactions

This article is concerned with the problem of state observer for complex large-scale systems with unknown time-varying delayed interactions. The class of large-scale interconnected systems under consideration is subjected to interval time-varying delays and nonlinear perturbations. By introducing a set of argumented Lyapunov–Krasovskii functionals and using a new bounding estimation technique, novel delay-dependent conditions for existence of state observers with guaranteed exponential stability are derived in terms of linear matrix inequalities (LMIs). In our design approach, the set of full-order Luenberger-type state observers are systematically derived via the use of an efficient LMI-based algorithm. Numerical examples are given to illustrate the effectiveness of the result

New H∞ control design for polytopic systems with mixed time-varying delays in state and input

This paper concerns with the problem of state-feedback H∞ control design for a class of linear systems with polytopic uncertainties and mixed time-varying delays in state and input. Our approach can be described as follows. We first construct a state-feedback controller based on the idea of parameter-dependent controller design. By constructing a new parameter-dependent Lyapunov-Krasovskii functional (LKF), we then derive new delay-dependent conditions in terms of linear matrix inequalities ensuring the exponential stability of the corresponding closed-loop system with a H∞ disturbance attenuation level. The effectiveness and applicability of the obtained results are demonstrated by practical examples.

Time-varying herding behavior, global financial crisis, and the Chinese stock market

In this paper, we examine the evidence of herding behavior on the Chinese stock market. Our main findings are as follows. First, we find strong evidence of herding behavior on both the Shanghai and Shenzhen stock exchanges. Second, we document evidence of asymmetric herding behavior with greater magnitude of herding behavior on up markets than on down markets. Third, our findings suggest that herding behavior is sector-specific and predominant in the industrial and properties sectors. Finally, we unravel strong evidence suggesting that herding behavior is time-varying and in some sectors time-varying herding behavior is more prevalent than in other sectors.

Synchronization of singular Markovian jumping complex networks with additive time-varying delays via pinning control

Abstract
This study examines the problem of synchronization for singular complex dynamical networks with Markovian jumping parameters and two additive time-varying delay components. The complex networks consist of m modes which switch from one mode to another according to a Markovian chain with known transition probability. Pinning control strategies are designed to make the singular complex networks synchronized. Based on the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices and using convexity of matrix functions, a novel synchronization criterion is derived. The proposed sufficient conditions are established in the form of linear matrix inequalities. Finally, a numerical example is presented to illustrate the effectiveness of the obtained results.

Exponential stability for markovian jumping stochastic BAM neural networks with mode-dependent probabilistic time-varying delays and impulse control

Abstract
In this article, an exponential stability analysis of Markovian jumping stochastic bidirectional associative memory (BAM) neural networks with mode-dependent probabilistic time-varying delays and impulsive control is investigated. By establishment of a stochastic variable with Bernoulli distribution, the information of probabilistic time-varying delay is considered and transformed into one with deterministic time-varying delay and stochastic parameters. By fully taking the inherent characteristic of such kind of stochastic BAM neural networks into account, a novel Lyapunov-Krasovskii functional is constructed with as many as possible positive definite matrices which depends on the system mode and a triple-integral term is introduced for deriving the delay-dependent stability conditions. Furthermore, mode-dependent mean square exponential stability criteria are derived by constructing a new Lyapunov-Krasovskii functional with modes in the integral terms and using some stochastic analysis techniques. The criteria are formulated in terms of a set of linear matrix inequalities, which can be checked efficiently by use of some standard numerical packages. Finally, numerical examples and its simulations are given to demonstrate the usefulness and effectiveness of the proposed results.

Channel estimation for time-varying MIMO relay systems

In this paper, we investigate the channel estimation problem for multiple-input multiple-output (MIMO) relay communication systems with time-varying channels. The time-varying characteristic of the channels is described by the complex-exponential basis expansion model (CE-BEM). We propose a superimposed channel training algorithm to estimate the individual first-hop and second-hop time-varying channel matrices for MIMO relay systems. In particular, the estimation of the second-hop time-varying channel matrix is performed by exploiting the superimposed training sequence at the relay node, while the first-hop time-varying channel matrix is estimated through the source node training sequence and the estimated second-hop channel. To improve the performance of channel estimation, we derive the optimal structure of the source and relay training sequences that minimize the mean-squared error (MSE) of channel estimation. We also optimize the relay amplification factor that governs the power allocation between the source and relay training sequences. Numerical simulations demonstrate that the proposed superimposed channel training algorithm for MIMO relay systems with time-varying channels outperforms the conventional two-stage channel estimation scheme.