Reliable H∞ control for discrete-time piecewise linear systems with infinite distributed delays

In this paper, the reliable H∞ control problem is investigated for discrete-time piecewise linear systems with time delays and actuator failures. The time delays are assumed to be infinitely distributed in the discrete-time domain, and the possible failure of each actuator is described by a variable varying in a given interval. The aim of the addressed reliable H∞ control problem is to design a controller such that, for the admissible infinite distributed delays and possible actuator failures, the closed-loop system is exponentially stable with a given disturbance attenuation level γ. The controller gain is characterized in terms of the solution to a linear matrix inequality that can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures

Empirical properties of inter-cancellation durations in the Chinese stock market

Order cancellation process plays a crucial role in the dynamics of price formation in order-driven stock markets and is important in the construction and validation of computational finance models. Based on the order flow data of 18 liquid stocks traded on the Shenzhen Stock Exchange in 2003, we investigate the empirical statistical properties of inter-cancellation durations in units of events defined as the waiting times between two consecutive cancellations. The inter-cancellation durations for both buy and sell orders of all the stocks favor a $q$-exponential distribution when the maximum likelihood estimation method is adopted; In contrast, both cancelled buy orders of 6 stocks and cancelled sell orders of 3 stocks prefer Weibull distribution when the nonlinear least-square estimation is used. Applying detrended fluctuation analysis (DFA), centered detrending moving average (CDMA) and multifractal detrended fluctuation analysis (MF-DFA) methods, we unveil that the inter-cancellation duration time series process long memory and multifractal nature for both buy and sell cancellations of all the stocks. Our findings show that order cancellation processes exhibit long-range correlated bursty behaviors and are thus not Poissonian.Comment: 14 pages, 7 figures and 5 table