Robust filtering for bilinear uncertain stochastic discrete-time systems

Copyright [2002] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper deals with the robust filtering problem for uncertain bilinear stochastic discrete-time systems with estimation error variance constraints. The uncertainties are allowed to be norm-bounded and enter into both the state and measurement matrices. We focus on the design of linear filters, such that for all admissible parameter uncertainties, the error state of the bilinear stochastic system is mean square bounded, and the steady-state variance of the estimation error of each state is not more than the individual prespecified value. It is shown that the design of the robust filters can be carried out by solving some algebraic quadratic matrix inequalities. In particular, we establish both the existence conditions and the explicit expression of desired robust filters. A numerical example is included to show the applicability of the present method

On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters

Copyright [2002] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, we investigate the stochastic stabilization problem for a class of bilinear continuous time-delay uncertain systems with Markovian jumping parameters. Specifically, the stochastic bilinear jump system under study involves unknown state time-delay, parameter uncertainties, and unknown nonlinear deterministic disturbances. The jumping parameters considered here form a continuous-time discrete-state homogeneous Markov process. The whole system may be regarded as a stochastic bilinear hybrid system that includes both time-evolving and event-driven mechanisms. Our attention is focused on the design of a robust state-feedback controller such that, for all admissible uncertainties as well as nonlinear disturbances, the closed-loop system is stochastically exponentially stable in the mean square, independent of the time delay. Sufficient conditions are established to guarantee the existence of desired robust controllers, which are given in terms of the solutions to a set of either linear matrix inequalities (LMIs), or coupled quadratic matrix inequalities. The developed theory is illustrated by numerical simulatio

The value premium puzzle, behavior versus risk: new evidence from China

This paper investigates the value premium puzzle in the Chinese stock market. After establishing that the value premium does exist in the Chinese stock market, it uses an innovative technique based on stochastic dominance theory to test the behavior based versus risk based explanations for the puzzle. We find no evidence of a systematic behavioral factor, such as over/under-reaction, that is driving this premium. This finding is robust with respect to negative and positive return regimes. We do, however, find strong evidence that the value premium reflects compensation for bearing more risk associated with financial inflexibility

On controllability of neuronal networks with constraints on the average of control gains

Control gains play an important role in the control of a natural or a technical system since they reflect how much resource is required to optimize a certain control objective. This paper is concerned with the controllability of neuronal networks with constraints on the average value of the control gains injected in driver nodes, which are in accordance with engineering and biological backgrounds. In order to deal with the constraints on control gains, the controllability problem is transformed into a constrained optimization problem (COP). The introduction of the constraints on the control gains unavoidably leads to substantial difficulty in finding feasible as well as refining solutions. As such, a modified dynamic hybrid framework (MDyHF) is developed to solve this COP, based on an adaptive differential evolution and the concept of Pareto dominance. By comparing with statistical methods and several recently reported constrained optimization evolutionary algorithms (COEAs), we show that our proposed MDyHF is competitive and promising in studying the controllability of neuronal networks. Based on the MDyHF, we proceed to show the controlling regions under different levels of constraints. It is revealed that we should allocate the control gains economically when strong constraints are considered. In addition, it is found that as the constraints become more restrictive, the driver nodes are more likely to be selected from the nodes with a large degree. The results and methods presented in this paper will provide useful insights into developing new techniques to control a realistic complex network efficiently

H∞ reliable control of uncertain linear state delayed systems

This is the post print version of the article. The official published version can be obtained from the link below - Copyright @ 2004 Springer Verlag.This paper deals with the problem of robust and reliable H control design for linear uncertain time-delay systems with time-varying norm-bounded parameter uncertainty, and also with actuator failures among a specified subset of actuators. A state feedback control design is presented that stabilizes the plant and guarantees an H -norm bound constraint on attenuation of the augmented disturbances, including failure signals, for all admissible uncertainties as well as actuator failures. It is shown that the existence of the desired controllers is related to the positive definite solution of a parameter-dependent Riccati-like matrix equation, whose solving algorithm is also discussed in detail. Two illustrative examples are provided to demonstrate the applicability of the proposed method.This work was partially supported by the EPSRC, Grant GR/S27658/01, the Nuffield Foundation, Grant NAL/00630/G, and the Alexander von Humboldt Foundation of Germany

Theories of risk: testing investor behaviour on the Taiwan stock and stock index futures markets

This paper considers four utility functions - concave, convex, S-shaped, and reverse S-shaped - to analyze the behavior of different types of investors on the Taiwan stock index and its corresponding index futures. Using stochastic dominance (SD) rules, we show that the existence of all four investor types is plausible. Risk averters prefer spot to futures, whereas risk seekers prefer futures to spot. Investors with S-shaped utility functions prefer spot (futures) to futures (spot) when markets move upward (downward). Investors with reverse S-shaped utility functions prefer futures (spot) to spot (futures) when markets move upward (downward). We show that both spot and futures markets can exist when only risk averters are present, but futures can dominate spot only if there is some risk seeking behavior. These results are robust with respect to sub-periods, spot returns including dividends and diversification