Event‐triggered filter design for Markovian jump delay systems with nonlinear perturbation using quantized measurement

This paper deals with the problem of mixed passivity and H_∞ filter design for a class of Markovian jump delay systems with nonlinear perturbation under event‐triggered scheme and quantization. Firstly, based on an integral inequality, a new sufficient condition for the stochastic stability and performance analysis of the filtering error system is proposed. Secondly, a mode‐dependent condition for the solvability of the filter design problem is given in terms of linear matrix inequalities (LMIs). The filter parameters can be derived using feasible solutions of the presented LMIs. Finally, three numerical examples are given to illustrate the effectiveness and advantages of the proposed filter design method.     

Exponential H∞ filtering for nonlinear discrete‐time switched stochastic systems with mixed time delays and random missing measurements

This paper is concerned with the exponential H_∞ filtering for a class of nonlinear discrete‐time switched stochastic hybrid systems with mixed time delays and random missing measurements. The switched system under study involves stochastic disturbance, time‐varying discrete delay, bounded distributed delay and nonlinearity. Attention is focused on the design of a mode‐dependent filter that guarantees the exponential stability in the mean‐square sense and a prescribed H_∞ noise attenuation level for the filtering error dynamics. By constructing a new Lyapunov functional and using the average dwell time scheme, a new delay‐dependent sufficient condition for the existence of the filter is presented in terms of linear matrix inequalities. A numerical example is finally given to show the effectiveness of the proposed design method. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Exponential H∞ filter design for stochastic time‐varying delay systems with Markovian jumping parameters

In this paper, the exponential H_∞ filter design problem is investigated for a general class of stochastic time‐varying delay system with Markovian jumping parameters. The stochastic uncertainties appear in both the dynamic and the measurement equations and the state delay is assumed to be time‐varying. Attention is focused on the design of mean‐square exponentially stable and Markovian jump filter such that the filtering error systems are mean‐square exponentially stable and the estimation error satisfies a given H_∞ performance. By introducing some slack matrix variables, delay‐dependent sufficient conditions for the solvability of the above problem are presented in terms of linear matrix inequalities (LMIs). In addition, the decay rate can be a given positive value without any other constraints. When the proposed LMIs are feasible, an explicit expression of the desired H_∞ filter can be given. A numerical example is provided to illustrate the effectiveness of the proposed design approach. Copyright © 2009 John Wiley & Sons, Ltd.     

Gain‐scheduled H∞ filtering of parameter‐varying systems

This paper deals with the gain‐scheduled H_∞ filtering problem for a class of parameter‐varying systems. A sufficient condition for the existence of a gain‐scheduled filter, which guarantees the asymptotic stability with an H_∞ noise attenuation level bound for the filtering error system, is given in terms of a finite number of linear matrix inequalities (LMIs). The filter is designed to be parameter‐varying and have a nonlinear fractional transformation structure. A numerical example is presented to demonstrate the application of the proposed method. Copyright © 2006 John Wiley & Sons, Ltd.     

Robust L2−L∞ Filtering for Stochastic Systems with Discrete and Distributed Time‐Varying Delays

This paper is devoted to the problem of robust L₂–L_∞ filtering for a class of stochastic systems with both discrete and distributed time‐varying delays. The objective is to design a full‐order filter such that the resulting filtering error system is stochastically asymptotically stable with a prescribed L₂–L_∞ performance satisfied. Delay‐dependent sufficient condition for the existence of the filter is obtained in terms of linear matrix inequalities (LMIs). And the filter design method is proposed, while the explicit expression for the desired filter is also given. Numerical examples are included to illustrate the benefit and the effectiveness of the proposed method. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Exponential H∞ Filtering for Discrete‐Time Switched State‐Delay Systems Under Asynchronous Switching

The exponential H_∞ filtering problem of discrete‐time switched state‐delay systems under asynchronous switching is considered in this paper. The objective is to design a full‐order or reduced‐order switched filter guaranteeing the exponential stability with the weighted H_∞ performance of the filtering error system. A sufficient condition for the exponential stability with the weighted H_∞ performance of the filtering error system is provided based on delay‐dependent multiple Lyapunov‐Krasovskii functionals. The gains of the filter can be obtained by solving a set of linear matrix inequalities. A numerical example is presented to demonstrate the effectiveness of the developed results.     

Exponential H∞ filtering for switched linear systems with interval time‐varying delay

This paper deals with the problem of exponential H_∞ filtering for a class of continuous‐time switched linear system with interval time‐varying delay. The time delay under consideration includes two cases: one is that the time delay is differentiable and bounded with a constant delay‐derivative bound, whereas the other is that the time delay is continuous and bounded. Switched linear filters are designed to ensure that the filtering error systems under switching signal with average dwell time are exponentially stable with a prescribed H_∞ noise attenuation level. Based on the free‐weighting matrix approach and the average dwell technology, delay‐dependent sufficient conditions for the existence of such a filter are derived and formulated in terms of linear matrix inequalities (LMIs). By solving that corresponding LMIs, the desired filter parameterized matrices and the minimal average dwell time are obtained. Finally, two numerical examples are presented to demonstrate the effectiveness of the developed results. Copyright © 2008 John Wiley & Sons, Ltd.     

Fuzzy model‐based fault detection for Markov jump systems

The robust fault detection filter (RFDF) design problems are studied for nonlinear stochastic time‐delay Markov jump systems. By means of the Takagi–Sugeno fuzzy models, the fuzzy RFDF system and the dynamics of filtering error generator are constructed. Moreover, taking into account the sensitivity to faults while guaranteeing robustness against unknown inputs, the H_∞ filtering scheme is proposed to minimize the influences of the unknown inputs and another new performance index is introduced to enhance the sensitivity to faults. A sufficient condition is first established on the stochastic stability using stochastic Lyapunov–Krasovskii function. Then in terms of linear matrix inequalities techniques, the sufficient conditions on the existence of fuzzy RFDF are presented and proved. Finally, the design problem is formulated as a two‐objective optimization algorithm. Simulation results illustrate that the proposed RFDF can detect the faults shortly after the occurrences. Copyright © 2008 John Wiley & Sons, Ltd.     

Exponential stability and exponential stabilization of singularly perturbed stochastic systems with time‐varying delay

In this paper, the problems of exponential stability and exponential stabilization for linear singularly perturbed stochastic systems with time‐varying delay are investigated. First, an appropriate Lyapunov functional is introduced to establish an improved delay‐dependent stability criterion. By applying free‐weighting matrix technique and by equivalently eliminating time‐varying delay through the idea of convex combination, a less conservative sufficient condition for exponential stability in mean square is obtained in terms of ε‐dependent linear matrix inequalities (LMIs). It is shown that if this set of LMIs for ε=0 are feasible then the system is exponentially stable in mean square for sufficiently small ε?0. Furthermore, it is shown that if a certain matrix variable in this set of LMIs is chosen to be a special form and the resulting LMIs are feasible for ε=0, then the system is ε‐uniformly exponentially stable for all sufficiently small ε?0. Based on the stability criteria, an ε‐independent state‐feedback controller that stabilizes the system for sufficiently small ε?0 is derived. Finally, numerical examples are presented, which show our results are effective and useful. Copyright © 2010 John Wiley & Sons, Ltd.     

传感器饱和的非线性网络化系统模糊\begin{document}$H_{\infty}$\end{document}滤波

研究了基于T-S模糊模型描述的非线性网络化系统$H_{\infty}$滤波器设计问题.由于网络诱导时滞的存在, 使得一个采样周期内, 到达接收端的数据可能是一个或多个, 也可能没有任何数据.提出传感器冗余策略解决由于饱和而引起的传感器件失效的问题.为降低结果的保守性, 选择模糊规则依赖的Lyapunov函数对滤波误差系统进行稳定性分析, 给出使滤波误差系统均方渐近稳定且具有指定$H_{\infty}$性能的充分条件, 滤波器参数通过求解一组线性矩阵不等式(Linear matrix inequalities, LMIs)得到.仿真研究结果表明算法的有效性.     

New results on delay‐dependent stability analysis and stabilization for stochastic time‐delay systems

This paper investigates the problems of stability analysis and stabilization for stochastic time‐delay systems. Firstly, this paper uses the martingale theory to investigate expectations of stochastic cross terms containing the Itô integral. On the basis of this, an improved delay‐dependent stability criterion is derived for stochastic delay systems. In the derivation process, the mathematical development avoids bounding stochastic cross terms, and neither model transformation method nor free‐weighting‐matrix method is used. Thus, the method leads to a simple criterion and shows less conservatism. Secondly, on the basis of this stability result, this paper further proposes a state‐feedback controller that exponentially stabilizes the stochastic delay system by a strict LMI. Therefore, unlike previous results, it is not necessary to transform the nonlinear matrix inequalities into LMIs by the cone complementarity linearization method or parameter‐tuning method, which always yield a suboptimal solution. Finally, examples are provided to demonstrate the reduced conservatism of the proposed conditions.Copyright © 2013 John Wiley & Sons, Ltd.     

Robust H∞ filtering of stochastic time‐delay systems with state dependent noise

This paper is concerned with the H_∞ filtering design for discrete‐time stochastic time‐delay systems with state dependent noise. A sufficient condition for the existence of H_∞ filter design is presented via linear matrix inequalities. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

H∞ filtering for a class of stochastic Markovian jump systems with impulsive effects

In this paper, we discuss the problem of H_∞ filtering for a class of stochastic Markovian jump systems with impulsive effects. The aim is to design a stochastically stable filter, using the locally sampled measurements, which guarantee both the stochastic stability and a prescribed level of H_∞ performance for the filtering error dynamics. A sufficient condition for the existence of such a filter is given in terms of certain linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired filter is obtained. A numerical example is provided to show the effectiveness of the proposed results. Copyright © 2007 John Wiley & Sons, Ltd.     

Delay‐range‐dependent robust H∞ filtering for uncertain systems with interval time‐varying delays

This paper is concerned with the problem of delay‐range‐dependent robust H_∞ filtering for systems with time‐varying delays in a range. The aim of this problem is to design a filter such that, for all admissible uncertainties, the filtering error system is robustly asymptotically stable with a prescribed H_∞ level. The desired filter can be constructed by solving a set of linear matrix inequalities (LMIs). An illustrative numerical example is provided to demonstrate the effectiveness of the proposed method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust H∞ filtering for uncertain impulsive stochastic systems under sampled measurements

This paper is concerned with the problem of robust H_∞ filtering for uncertain impulsive stochastic systems under sampled measurements. The parameter uncertainties are assumed to be time-varying norm-bounded. The aim is to design a stochastically stable filter, using the locally sampled measurements, which ensures both the robust stochastic stability and a prescribed level of H_∞ performance for the filtering error dynamics for all admissible uncertainties. A sufficient condition for the existence of such a filter is proposed in terms of certain linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired filter is given. An example is provided to demonstrate the effectiveness of the proposed approach.     

Delay‐dependent robust stability for stochastic time‐delay systems with polytopic uncertainties

This paper considers a delay‐dependent and parameter‐dependent robust stability criterion for stochastic time‐delay systems with polytopic uncertainties. The delay‐dependent robust stability criterion, as expressed in terms of linear matrix inequalities (LMIs), is obtained by using parameter‐dependent Lyapunov functions. It is shown that the result derived by a parameter‐dependent Lyapunov functional is less conservative. Numerical examples are provided to illustrate the effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

Distributed output-feedback controllers design for Markovian jump systems interconnected over an undirected graph with time-varying delay

This paper considers the problems of stochastic stability analysis and distributed output-feedback controllers design for Markovian jump systems interconnected over an undirected graph with state time-varying delay. Specifically, a sufficient condition for the well-posedness, stochastic stability and contractiveness of the resultant closed-loop system is first developed in the form of non-linear matrix inequalities. Then, to avoid the difficulty of solving non-linear matrix inequalities, the sufficient condition is relaxed to an equivalent one in terms of coupling linear matrix inequalities (LMIs), which provides an effective way to confirm the existence of a distributed output-feedback controller inheriting the structure of the given plant. Furthermore, a constructive algorithm is given for the design of such a distributed output-feedback controller to achieve the well-posedness, stochastic stability as well as the contractiveness of the corresponding closed-loop system. Finally, numerical simulations are given to illustrate the validity of the proposed method.     

A new design of delay‐dependent robust ℋ︁∞ filtering for continuous‐time polytopic systems with time‐varying delay

This paper revisits the problem of delay‐dependent robust ?_∞ filtering design for a class of continuous‐time polytopic linear systems with a time‐varying state delay. Based on a newly developed parameter‐dependent Lyapunov–Krasovskii functional combined with Projection Lemma and an improved free‐weighting matrix technique for delay‐dependent criteria, a new sufficient condition for robust ?_∞ performance analysis is first derived and then the filter synthesis is developed by using a simple matrix inequality linearization technique. It is shown that the desired filters can be constructed by solving a set of linear matrix inequalities. Finally, two simulation examples are given to show the effectiveness and less conservatism of the proposed method in comparison with the existing approaches. Copyright © 2009 John Wiley & Sons, Ltd.     

Stability and stabilization of discrete‐time singular Markov jump systems with time‐varying delay

The stochastic stability and stochastic stabilization of time‐varying delay discrete‐time singular Markov jump systems are discussed. For full and partial knowledge of transition probabilities cases, delay‐dependent linear matrix inequalities (LMIs) conditions for the systems to be regular, causal and stochastically stable are given. Sufficient conditions are proposed for the existence of state feedback controller in terms of LMIs. Finally, two numerical examples to illustrate the effectiveness of the method are given. Copyright © 2009 John Wiley & Sons, Ltd.     

Polynomial filtering for nonlinear stochastic systems with state‐ and disturbance‐dependent noises

This article is concerned with the polynomial filtering problem for a class of nonlinear stochastic systems governed by the Itô differential equation. The system under investigation involves polynomial nonlinearities, unknown‐but‐bounded disturbances, and state‐ and disturbance‐dependent noises ((x,d)‐dependent noises for short). By expanding the polynomial nonlinear functions in Taylor series around the state estimate, a new polynomial filter design method is developed with hope to reduce the conservatism of the existing results. In virtue of stochastic analysis and inequality technique, sufficient conditions in terms of parameter‐dependent linear matrix inequalities (PDLMIs) are derived to guarantee that the estimation error system is input‐to‐state stable in probability. Moreover, the desired polynomial matrix can be obtained by solving the PDLMIs via the sum‐of‐squares approach. The effectiveness and applicability of the proposed method are illustrated by two numerical examples with one concerning the permanent magnet synchronous motor.