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

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.

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.

Dynamical analysis of neural networks with time-varying delays using the LMI approach

This study is concerned with the delay-range-dependent stability analysis for neural networks with time-varying delay and Markovian jumping parameters. The time-varying delay is assumed to lie in an interval of lower and upper bounds. The Markovian jumping parameters are introduced in delayed neural networks, which are modeled in a continuous-time along with finite-state Markov chain. Moreover, the sufficient condition is derived in terms of linear matrix inequalities based on appropriate Lyapunov-Krasovskii functionals and stochastic stability theory, which guarantees the globally asymptotic stable condition in the mean square. Finally, a numerical example is provided to validate the effectiveness of the proposed conditions.

Reachable sets bounding for switched systems with time-varying delay and bounded disturbances

In this paper, we address the problem of finding outer bound of forward reachable sets and inter-bound of backward reachable sets of switched systems with an interval time-varying delay and bounded disturbances. By constructing a flexible Lyapunov–Krasovskii functional combining with some recent refined integral-based inequalities, some sufficient conditions are derived for the existence of (1) the smallest possible outer bound of forwards reachable sets; and (2) the largest possible inter-bound of backward reachable sets. These conditions are delay dependent and in the form of linear matrix inequalities, which therefore can be efficiently solved by using existing convex algorithms. A constructive geometric design of switching laws is also presented. Two numerical examples with simulation results are provided to demonstrate the effectiveness of our results.

New inequality-based approach to passivity analysis of neural networks with interval time-varying delay

This paper is concerned with the problem of passivity analysis of neural networks with an interval time-varying delay. Unlike existing results in the literature, the time-delay considered in this paper is subjected to interval time-varying without any restriction on the rate of change. Based on novel refined Jensen inequalities and by constructing an improved Lyapunov-Krasovskii functional (LKF), which fully utilizes information of the neuron activation functions, new delay-dependent conditions that ensure the passivity of the network are derived in terms of tractable linear matrix inequalities (LMIs) which can be effectively solved by various computational tools. The effectiveness and improvement over existing results of the proposed method in this paper are illustrated through numerical examples.

Superimposed channel training algorithm for time-varying MIMO relay systems

Two-way relaying systems are known to be capable of providing higher spectral efficiency compared with one-way relaying systems. However, the channel estimation problem for two-way relaying systems becomes more complicated. In this paper, we propose a superimposed channel training scheme for two-way MIMO relay communication systems, where the individ-ual channel information for users-relay and relay-users links are estimated. The optimal structure of the source and relay training sequences are derived when the mean-squared error (MSE) of channel estimation is minimized. We also optimize the power allocation between the source and relay training sequences to improve the performance of the algorithm. Numerical examples are shown to demonstrate the performance of the proposed channel training algorithm.

Predictive motion planning for AUVs subject to strong time-varying currents and forecasting uncertainties

This paper presents a novel path planning method for minimizing the energy consumption of an autonomous underwater vehicle subjected to time varying ocean disturbances and forecast model uncertainty. The algorithm determines 4-Dimensional path candidates using Nonlinear Robust Model Predictive Control (NRMPC) and solutions optimised using A∗-like algorithms. Vehicle performance limits are incorporated into the algorithm with disturbances represented as spatial and temporally varying ocean currents with a bounded uncertainty in their predictions. The proposed algorithm is demonstrated through simulations using a 4-Dimensional, spatially distributed time-series predictive ocean current model. Results show the combined NRMPC and A∗ approach is capable of generating energy-efficient paths which are resistant to both dynamic disturbances and ocean model uncertainty.

Passivity analysis of memristor-based complex-valued neural networks with time-varying delays

In this paper, the model of memristor-based complex-valued neural networks (MCVNNs) with time-varying delays is established and the problem of passivity analysis for MCVNNs is considered and extensively investigated. The analysis in this paper employs results from the theory of differential equations with discontinuous right-hand side as introduced by Filippov. By employing the appropriate Lyapunov–Krasovskii functional, differential inclusion theory and linear matrix inequality (LMI) approach, some new sufficient conditions for the passivity of the given MCVNNs are obtained in terms of both complex-valued and real-value LMIs, which can be easily solved by using standard numerical algorithms. Numerical examples are provided to illustrate the effectiveness of our theoretical results.

Partial state bounding with a pre-specified time of non-linear discrete systems with time-varying delays

In this study, the authors address a new problem of finding, with a pre-specified time, bounds of partial states of non-linear discrete systems with a time-varying delay. A novel computational method for deriving the smallest bounds is presented. The method is based on a new comparison principle, a new algorithm for finding the infimum of a fractal function, and linear programming. The effectiveness of our obtained results is illustrated through a numerical example.