Robust Control of Uncertain Time -Delay Systems.

Time-delay systems are common in industries. Direct analysis and synthesis of control systems with time delays are complicated and approximation methods such as Pade approximation are usually applied. However, the issues of control system robustness with respect to model uncertainties and approximation errors have not been sufficiently addressed. This dissertation focus on robustness of time-delay systems, especially robustness with respect to time delays, which has been discussed extensively using Lyapunov second method. We propose two methods in this dissertation to reformulate the problems into standard mu or Hinfinity problems. The first method involves representing the systems in linear functional transformation (LFT) framework and approximating delays by rational transfer functions. The approximation errors are then treated as uncertainties. We show that all the well-known techniques of Hinfinity control theory can be applied to this framework. Consequently, controller design becomes a routine process. We also show that the conventional Lyapunov method is a special case in our proposed framework and our proposed method offers less conservative results. In the second method, we treat uncertain delays as uncertainties with restricted phase angles and extend structured singular value to include phase information. We show that the extended small-mu theorem can be applied to analyze stability and performance of uncertain delay systems with many other type of uncertainties, such as plant model uncertainties and parametric uncertainties. Finally, we generalize the above techniques to linear systems with feedback connected nonlinear elements. Both time invariant and time-varying nonlinearities are discussed by incorporating circle/Popov criterion with small-mu theorem

Self-organization and phase transition in financial markets with multiple choices

Market confidence is essential for successful investing. By incorporating multi-market into the evolutionary minority game, we investigate the effects of investor beliefs on the evolution of collective behaviors and asset prices. When there exists another investment opportunity, market confidence, including overconfidence and under-confidence, is not always good or bad for investment. The roles of market confidence is closely related to market impact. For low market impact, overconfidence in a particular asset makes an investor become insensitive to losses and a delayed strategy adjustment leads to a decline in wealth, and thereafter, one's runaway from the market. For high market impact, under-confidence in a particular asset makes an investor over-sensitive to losses and one's too frequent strategy adjustment leads to a large fluctuation in asset prices, and thereafter, a decrease in the number of agents. At an intermediate market impact, the phase transition occurs. No matter what the market impact is, an equilibrium between different markets exists, which is reflected in the occurrence of similar price fluctuations in different markets. A theoretical analysis indicates that such an equilibrium results from the coupled effects of strategy updating and shift in investment. The runaway of the agents trading a specific asset will lead to a decline in the asset price volatility and such a decline will be inhibited by the clustering of the strategies. A uniform strategy distribution will lead to a large fluctuation in asset prices and such a fluctuation will be suppressed by the decrease in the number of agents in the market. A functional relationship between the price fluctuations and the numbers of agents is found

Influence of unsymmetrical periodicity on extraordinary transmission through periodic arrays of subwavelength holes

Quadrate hole array is explored to study the influence of unsymmetrical periodicity on extraordinary optical transmission through periodic arrays of subwavelength holes. It is found that the transmission efficiency of light and the ratio between transmission efficiencies of horizontal and vertical polarized light can be continuously tuned by rotating the quadrate hole array. We can calculate out the transmission spectra (including the heights and locations of peaks) for any rotation angle $\theta$ with a simple theoretical model.Comment: 6 pages, 5 figure

A lost decade for third-wave democracies?

By comparing results based on expert and popular surveys, this article finds that popular support for democracy was dwindling even in the decade before expert surveys (such as Freedom in the World and V-Dem) began to show the reality of democratic retreat. Decreasing support for democracy is tied to low satisfaction with how democracy works in practice, and it contributes to the rise of populist leaders who concentrate power in the executive branch. These phenomena reflect the waning capacity of the state to improve governance across all countries. As a result, democracy is likely to face another lackluster decade if both structural and institutional problems are left unsolved

Interference of surface plasmon polaritions controlled by the phase of incident light

Interference patterns of surface plasmon polaritons(SPPs) are observed in the extraordinary optical transmission through subwavelength holes in optically thick metal plate. It is found that the phase of incident light can be transferred to SPPs. We can control the destructive and constructive interference of SPPs by modulating the relative phase between two incident beams. Using a slightly displaced Mach-Zehnder interferometer, we also observe a SPPs interference pattern composed of bright and dark stripes.Comment: 3pages,5figure