Exponential stabilization of a class of stochastic system with Markovian jump parameters and mode-dependent mixed time-delays

Copyright [2010] 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 technical note, the globally exponential stabilization problem is investigated for a general class of stochastic systems with both Markovian jumping parameters and mixed time-delays. The mixed mode-dependent time-delays consist of both discrete and distributed delays. We aim to design a memoryless state feedback controller such that the closed-loop system is stochastically exponentially stable in the mean square sense. First, by introducing a new Lyapunov-Krasovskii functional that accounts for the mode-dependent mixed delays, stochastic analysis is conducted in order to derive a criterion for the exponential stabilizability problem. Then, a variation of such a criterion is developed to facilitate the controller design by using the linear matrix inequality (LMI) approach. Finally, it is shown that the desired state feedback controller can be characterized explicitly in terms of the solution to a set of LMIs. Numerical simulation is carried out to demonstrate the effectiveness of the proposed methods.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., the National 973 Program of China under Grant 2009CB320600, and the Alexander von Humboldt Foundation of Germany. Recommended by Associate Editor G. Chesi

On passivity and passification of stochastic fuzzy systems with delays: The discrete-time case

Copyright [2010] 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.Takagi–Sugeno (T-S) fuzzy models, which are usually represented by a set of linear submodels, can be used to describe or approximate any complex nonlinear systems by fuzzily blending these subsystems, and so, significant research efforts have been devoted to the analysis of such models. This paper is concerned with the passivity and passification problems of the stochastic discrete-time T-S fuzzy systems with delay. We first propose the definition of passivity in the sense of expectation. Then, by utilizing the Lyapunov functional method, the stochastic analysis combined with the matrix inequality techniques, a sufficient condition in terms of linear matrix inequalities is presented, ensuring the passivity performance of the T-S fuzzy models. Finally, based on this criterion, state feedback controller is designed, and several criteria are obtained to make the closed-loop system passive in the sense of expectation. The results acquired in this paper are delay dependent in the sense that they depend on not only the lower bound but also the upper bound of the time-varying delay. Numerical examples are also provided to demonstrate the effectiveness and feasibility of our criteria.This work was supported in part by the Royal Society Sino–British Fellowship Trust Award of the U.K., by the National Natural Science Foundation of China under Grant 60804028, by the Specialized Research Fund for the Doctoral Program of Higher Education for New Teachers in China under Grant 200802861044, and by the Teaching and Research Fund for Excellent Young Teachers at Southeast University of China

The impact of tax uncertainty on irreversible investment

Traditional models of capital budgeting including taxes are based on deterministic tax rates and tax bases. In reality, however, there are multiple sources of tax uncertainty. Tax reforms induce frequent changes in both tax rates and tax bases, making future taxation of investments a stochastic process. Fiscal authorities and tax courts create additional tax uncertainty by interpreting current tax laws differently. Apart from fiscal tax uncertainty, there is modelspecific tax uncertainty, because investors use simplified models for computing an investment project's tax base and anticipate the actual tax base incorrectly. I analyze the effects of stochastic taxation on investment behaviour in a real options model. The potential investor holds an option to invest in an irreversible project with stochastic cash flows. To cover the combined effects of tax base and tax rate uncertainty, the investment's tax payment is modelled as a stochastic process that may be correlated with the project's cash flows. I show that increased uncertainty of tax payments has an ambiguous impact on investment timing. Thus, the popular view that tax uncertainty depresses real investment can be rejected. For low tax uncertainty, high cash flow uncertainty and high correlation of cash flows and tax payment, increased tax uncertainty may even accelerate investment. A higher expected tax payment delays investment. Surprisingly, a higher tax rate on interest income affects investment timing ambiguously. --

The Impact of Tax Uncertainty on Irreversible Investment

Tax legislation, fiscal authorities, and tax courts create tax uncertainty by frequent tax reforms and various different interpretations of the tax law. Moreover, investors generate model-specific tax uncertainty by using simplified models that anticipate the actual tax base incorrectly. I analyze the effects of stochastic taxation on investment behavior in a real options model. The investor holds an option to invest in an irreversible project with stochastic cash flows. To cover the effects of both tax base and tax rate uncertainty, the investment’s tax payment is modelled as a stochastic process. Increased tax uncertainty has an ambiguous impact on investment timing. The view that tax uncertainty depresses real investment is rejected. A higher expected tax payment delays investment. A higher tax rate on interest income affects investment timing ambiguously.tax uncertainty, capital budgeting, real options, investment incentives

On the moment dynamics of stochastically delayed linear control systems

In this article, the dynamics and stability of a linear system with stochastic delay and additive noise are investigated. It is assumed that the delay value is sampled periodically from a stationary distribution. A semi‐discretization technique is used to time‐discretize the system and derive the mean and second‐moment dynamics. These dynamics are used to obtain the stationary moments and the corresponding necessary and sufficient stability conditions. The application of the proposed method is illustrated through the analysis of the Hayes equation with stochastic delay and additive noise. The method is also applied to the control design of a connected automated vehicle. These examples illuminate the effects of stochastic delays on the robustness of dynamical systems

Effective drifts in dynamical systems with multiplicative noise: A review of recent progress

Noisy dynamical models are employed to describe a wide range of phenomena. Since exact modeling of these phenomena requires access to their microscopic dynamics, whose time scales are typically much shorter than the observable time scales, there is often need to resort to effective mathematical models such as stochastic differential equations (SDEs). In particular, here we consider effective SDEs describing the behavior of systems in the limits when natural time scales become very small. In the presence of multiplicative noise (i.e. noise whose intensity depends upon the system's state), an additional drift term, called noise-induced drift or effective drift, appears. The nature of this noise-induced drift has been recently the subject of a growing number of theoretical and experimental studies. Here, we provide an extensive review of the state of the art in this field. After an introduction, we discuss a minimal model of how multiplicative noise affects the evolution of a system. Next, we consider several case studies with a focus on recent experiments: the Brownian motion of a microscopic particle in thermal equilibrium with a heat bath in the presence of a diffusion gradient; the limiting behavior of a system driven by a colored noise modulated by a multiplicative feedback; and the behavior of an autonomous agent subject to sensorial delay in a noisy environment. This allows us to present the experimental results, as well as mathematical methods and numerical techniques, that can be employed to study a wide range of systems. At the end we give an application-oriented overview of future projects involving noise-induced drifts, including both theory and experiment. © 2016 IOP Publishing Ltd

Dissipativity analysis of stochastic fuzzy neural networks with randomly occurring uncertainties using delay dividing approach

This paper focuses on the problem of delay-dependent robust dissipativity analysis for a class of stochastic fuzzy neural networks with time-varying delay. The randomly occurring uncertainties under consideration are assumed to follow certain mutually uncorrelated Bernoulli-distributed white noise sequences. Based on the Itô's differential formula, Lyapunov stability theory, and linear matrix inequalities techniques, several novel sufficient conditions are derived using delay partitioning approach to ensure the dissipativity of neural networks with or without time-varying parametric uncertainties. It is shown, by comparing with existing approaches, that the delay-partitioning projection approach can largely reduce the conservatism of the stability results. Numerical examples are constructed to show the effectiveness of the theoretical results