Finite‐time H ∞ filtering for a class of discrete‐time Markovian jump systems with partly unknown transition probabilities

This paper is concerned with the problem of finite‐time H _∞ filtering for a class of Markovian jump systems subject to partial information on the transition probabilities. By introducing some slack matrix variables in terms of probability identity, a less conservative bounded real lemma is derived to ensure that filtering Markovian jump systems is finite‐time stable. Finally, the existence criterion of the desired filter is obtained such that the corresponding filtering error system is finite‐time bounded with a guaranteed H _∞ performance index. An example is given to illustrate the efficiency of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Passivity analysis of neural networks with two different Markovian jumping parameters and mixed time delays

This paper studies the problem of passivity analysis for neural networks with two different Markovian jumping parameters and mixed time delays utilizing some integral inequalities. The integral inequalities produce sharper bounds than what the Jensen's inequality produces, consequently, better results are obtained. The Markovian jumping parameters in connection weight matrices and discrete delay are assumed to be different in the system model. By constructing a new appropriate Lyapunov-Krasovskii functional (LKF), some sufficient conditions are established which guarantee the passivity of the proposed model. Numerical examples are given to show the less conservatism and effectiveness of the proposed method.     

Stability and stabilization for singularly perturbed systems with Markovian jumps

This article focuses on the stability and stabilization problems of singularly perturbed jump systems. Here, the singularly perturbed parameter (SPP) is also with Markov switching and satisfies any with positive bound predefined. First, stability conditions expressed ?_i‐free but involving its bound are developed by constructing an ?_i‐dependent Lyapunov function. Then, a method for state feedback stabilization controller depending on SPP is proposed, whose conditions are given in terms of linear matrix inequalities. Moreover, some special cases about deterministic SPP are considered too. Finally, two practical examples are used to demonstrate the effectiveness and superiorities of the proposed methods.     

Sliding mode control for Markovian jumping systems with actuator nonlinearities

This article considers the design of sliding mode control for stochastic Markovian jumping systems with actuator nonlinearities. In the design of integral sliding surfaces, a set of specified matrices are employed such that the connections among sliding surfaces corresponding to each mode are established. And then, a sliding mode controller depending on the transition rates is synthesised such that the reachability of the specified sliding surface can be ensured. Moreover, sufficient conditions for the stability of the sliding motions are derived. It is shown that the effect of Markovian switching can be coped with by the present sliding mode control method. Finally, the simulation results illustrating the proposed method are provided.     

On Prediction Intervals for Conditionally Heteroscedastic Processes

Kabaila (1999) argues that the standard 1−α prediction intervals for a broad class of conditionally heteroscedastic processes are justified by their possession of what he calls the 'relevance property'. He considers both the case that the parameters of the process are known and that these parameters are unknown. We consider the former case and ask whether these prediction intervals can, alternatively, be deduced from the requirements of both (a) unconditional coverage probability 1−α and (b) minimum unconditional expected length. We show that the answer to this question is no, by presenting a counterexample. This counterexample concerns the standard 95% one-step-ahead prediction interval in the context of a simple Markovian bilinear process.     

Design of robust reliable control for T-S fuzzy Markovian jumping delayed neutral type neural networks with probabilistic actuator faults and leakage delays: An event-triggered communication scheme

This study examines the problem of robust reliable control for Takagi-Sugeno (T-S) fuzzy Markovian jumping delayed neural networks with probabilistic actuator faults and leakage terms. An event-triggered communication scheme. First, the randomly occurring actuator faults and their failures rates are governed by two sets of unrelated random variables satisfying certain probabilistic failures of every actuator, new type of distribution based event triggered fault model is proposed, which utilize the effect of transmission delay. Second, Takagi-Sugeno (T-S) fuzzy model is adopted for the neural networks and the randomness of actuators failures is modeled in a Markov jump model framework. Third, to guarantee the considered closed-loop system is exponential mean square stable with a prescribed reliable control performance, a Markov jump event-triggered scheme is designed in this paper, which is the main purpose of our study. Fourth, by constructing appropriate Lyapunov-Krasovskii functional, employing Newton-Leibniz formulation and integral inequalities, several delay-dependent criteria for the solvability of the addressed problem are derived. The obtained stability criteria are stated in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Finally, numerical examples are given to illustrate the effectiveness and reduced conservatism of the proposed results over the existing ones, among them one example was supported by real-life application of the benchmark problem.     

Finite-time stability and stabilization for stochastic markov jump systems with mode-dependent time delays

This paper is concerned with the problems of finite-time stability and stabilization for stochastic Markov systems with mode-dependent time-delays. In order to reduce conservatism, a mode-dependent approach is utilized. Based on the derived stability conditions, state-feedback controller and observer-based controller are designed, respectively. A new N-mode algorithm is given to obtain the maximum value of time-delay. Finally, an example is used to show the merit of the proposed results.     

Extension of some MAP results to transient MAPs and Markovian binary trees

In this work we extend previous results on moment-based characterization and minimal representation of stationary Markovian arrival processes (MAPs) and rational arrival processes (RAPs) to transient Markovian arrival processes (TMAPs) and Markovian binary trees (MBTs).     

计算机马尔柯夫销售预测法及其程序设计

本文对时间、状态离散的马尔柯夫过程,即马尔柯夫链及其计算机编程过程和如何利用该程序进行销售预测等做了研究。     

ROBUST H∞ CONTROL FOR UNCERTAIN STOCHASTIC SYSTEMS WITH MARKOVIAN SWITCHING AND TIME‐VARYING DELAYS

This paper is concerned with the problem of robust H_∞ control for uncertain stochastic systems with Markovian jump parameters and time‐varying state delays. A linear matrix inequality approach is developed and state feedback controllers are designed, which guarantee mean square asymptotic stability of the closed‐loop system and a prescribed H_∞ performance level for all modes and admissible uncertainties. A numerical example is provided to demonstrate the application of the proposed method.