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.

A study on time-varying quantile and its applications

This Thesis is the result of my Master Degree studies at the Graduate School of Economics, Getúlio Vargas Foundation, from January 2004 to August 2006. am indebted to my Thesis Advisor, Professor Luiz Renato Lima, who introduced me to the Econometrics' world. In this Thesis, we study time-varying quantile process and we develop two applications, which are presented here as Part and Part II. Each of these parts was transformed in paper. Both papers were submitted. Part shows that asymmetric persistence induces ARCH effects, but the LMARCH test has power against it. On the other hand, the test for asymmetric dynamics proposed by Koenker and Xiao (2004) has correct size under the presence of ARCH errors. These results suggest that the LM-ARCH and the Koenker-Xiao tests may be used in applied research as complementary tools. In the Part II, we compare four different Value-at-Risk (VaR) methodologies through Monte Cario experiments. Our results indicate that the method based on quantile regression with ARCH effect dominates other methods that require distributional assumption. In particular, we show that the non-robust method ologies have higher probability to predict VaRs with too many violations. We illustrate our findings with an empirical exercise in which we estimate VaR for returns of São Paulo stock exchange index, IBOVESPA, during periods of market turmoil. Our results indicate that the robust method based on quantile regression presents the least number of violations.

Um modelo "time-varying markov-Switching" para crescimento econômico e algoritmo de estimação

Este trabalho elabora um modelo para investigação do padrão de variação do crescimento econômico, entre diferentes países e através do tempo, usando um framework Markov- Switching com matriz de transição variável. O modelo desenvolvido segue a abordagem de Pritchett (2003), explicando a dinâmica do crescimento a partir de uma coleção de diferentes estados – cada qual com seu sub-modelo e padrão de crescimento – através dos quais os países oscilam ao longo do tempo. A matriz de transição entre os diferentes estados é variante no tempo, dependendo de variáveis condicionantes de cada país e a dinâmica de cada estado é linear. Desenvolvemos um método de estimação generalizando o Algoritmo EM de Diebold et al. (1993) e estimamos um modelo-exemplo em painel com a matriz de transição condicionada na qualidade das instituições e no nível de investimento. Encontramos três estados de crescimento: crescimento estável, ‘milagroso’ e estagnação - virtualmente coincidentes com os três primeiros de Jerzmanowski (2006). Os resultados mostram que a qualidade das instituições é um importante determinante do crescimento de longo prazo enquanto o nível de investimento tem papel diferenciado: contribui positivamente em países com boa qualidade de instituições e tem papel pouco relevante para os países com instituições medianas ou piores.

A time-varying markov-switching model for economic growth

This paper investigates economic growth’s pattern of variation across and within countries using a Time-Varying Transition Matrix Markov-Switching Approach. The model developed follows the approach of Pritchett (2003) and explains the dynamics of growth based on a collection of different states, each of which has a sub-model and a growth pattern, by which countries oscillate over time. The transition matrix among the different states varies over time, depending on the conditioning variables of each country, with a linear dynamic for each state. We develop a generalization of the Diebold’s EM Algorithm and estimate an example model in a panel with a transition matrix conditioned on the quality of the institutions and the level of investment. We found three states of growth: stable growth, miraculous growth, and stagnation. The results show that the quality of the institutions is an important determinant of long-term growth, whereas the level of investment has varying roles in that it contributes positively in countries with high-quality institutions but is of little relevance in countries with medium- or poor-quality institutions.

Recurrence of particles in static and time varying oval billiards

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)