Robust H∞ Filtering For Uncertain Stochastic Time‐Delay Systems

This paper deals with the problem of robust H_∞ filtering for uncertain stochastic systems. The system under consideration is subject to time‐varying norm‐bounded parameter uncertainties and unknown time delays in both the state and measurement equations. The problem we address is the design of a stable filter that ensures the robust stochastic stability and a prescribed H_∞ performance level for the filtering error system irrespective of all admissible uncertainties and time delays. A suffient condition for the solvability of this problem is proposed and a linear matrix inequality approach is developed for the design of the robust H_∞ filters. An illustrative example is provided to demonstrate the effctiveness of the proposed approach.     

Reliable H ∞ filter design for a class of mixed-delay Markovian jump systems with stochastic nonlinearities and multiplicative noises via delay-partitioning method

This paper is concerned with the problem of reliable H _?? filter design for a class of mixeddelay Markovian jump systems with stochastic nonlinearities and multiplicative noises. The mixed delays comprise both discrete time-varying delay and distributed delay. The stochastic nonlinearities in the form of statistical means cover several well-studied nonlinear functions. And the multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. Furthermore, the failures of sensors are quantified by a variable varying in a given interval. A filter is designed to guarantee that the dynamics of the estimation error is asymptotically mean-square stable. Sufficient conditions for the existence of such a filter are obtained by using a new Lyapunov-Krasovskii functional and delaypartitioning method. Then a linear matrix inequality (LMI) approach for designing such a reliable H _?? filter is presented. Finally, the effectiveness of the proposed approach is demonstrated by a numerical example.     

Local design of distributed H∞‐consensus filtering over sensor networks under multiplicative noises and deception attacks

This paper is concerned with the local design of the distributed H_∞‐consensus filtering problem for a class of discrete time‐varying systems subject to both multiplicative noises and deception attacks over sensor networks. The target plant and the measuring sensors are disturbed by multiplicative noises with known statistics. The malicious signal involved in deception attacks is constrained by a specific sector‐like bounded condition, which reflects certain tolerable bound on the difference between the attack signal and the true signal. Attention is paid to the design of filter gains for guaranteeing a desirable filtering performance that simultaneously characterizes the filtering accuracy and the consensus requirement. To handle the proposed filtering problem, the supply rate function is firstly chosen for each node and then the dissipation matrix is constructed as a column substochastic matrix based on the stochastic vector dissipation theory. Subsequently, sufficient conditions by means of recursive linear matrix inequalities are presented for each node such that the filtering error and the consensus error satisfy the desirable H_∞‐consensus performance index over a finite horizon. Finally, an illustrative simulation is presented to demonstrate the effectiveness of the proposed filter strategy.     

H∞ filtering for uncertain time‐varying systems with multiple randomly occurred nonlinearities and successive packet dropouts

This paper is concerned with the robust H_∞ finite‐horizon filtering problem for discrete time‐varying stochastic systems with multiple randomly occurred sector‐nonlinearities (MROSNs) and successive packet dropouts. MROSNs are proposed to model a class of sector‐like nonlinearities that occur according to the multiple Bernoulli distributed white sequences with a known conditional probability. Different from traditional approaches, in this paper, a time‐varying filter is designed directly for the addressed system without resorting to the augmentation of system states and measurement, which helps reduce the filter order. A new H_∞ filtering technique is developed by means of a set of recursive linear matrix inequalities that depend on not only the current available state estimate but also the previous measurement, therefore ensuring a better accuracy. Finally, two illustrative examples are used to demonstrate the effectiveness and applicability of the proposed filter design scheme. Copyright © 2010 John Wiley & Sons, Ltd.     

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     

Robust H∞ deconvolution filtering for uncertain singular Markovian jump systems with time‐varying delays

The problem of H_∞ deconvolution filter design for a class of singular Markovian jump systems with time‐varying delays and parameter uncertainties is considered in this paper. By constructing a more comprehensive stochastic Lyapunov‐Krasovskii functional, novel delay‐dependent conditions are established to guarantee the filtering error system is not only stochastically admissible, but also satisfies a prescribed H_∞‐norm level for all admissible uncertainties. The desired filter parameters can be obtained by solving a set of strict linear matrix inequalities. Two examples and an electrical RLC circuit example are employed to verify the effectiveness and usefulness of the proposed methods in the paper. Copyright © 2015 John Wiley & Sons, Ltd.     

Finite‐Time H∞ Filtering for Nonlinear Continuous‐Time Singular Semi‐Markov Jump Systems

The stochastic finite‐time H_∞ filtering issue for a class of nonlinear continuous‐time singular semi‐Markov jump systems is discussed in this paper. Firstly, sufficient conditions on singular stochastic H_∞ finite‐time boundedness for the filtering error system are established. The existence of a unique solution for the corresponding system is also ensured. Secondly, based on the bounds of the time‐varying transition rate, without imposing constraints on slack variables, a novel approach to finite‐time H_∞ filter design is proposed in the forms of strict LMIs, which guarantees the filtering error system is singular stochastic H_∞ finite‐time bounded and of a unique solution. Compared with the existing ones, the presented results reveal less conservativeness. Finally, one numerical example is exploited to testify the advantage of the proposed design technique.     

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     

State‐saturated H∞ filtering with randomly occurring nonlinearities and packet dropouts: the finite‐horizon case

This paper deals with the H_∞ filtering problem for a class of discrete time‐varying systems with state saturations, randomly occurring nonlinearities as well as successive packet dropouts. Two mutually independent sequences of random variables that obey the Bernoulli distribution are employed to describe the random occurrence of the nonlinearities and packet dropouts. The purpose of the addressed problem is to design a time‐varying filter such that the H_∞ disturbance attenuation level is guaranteed, over a given finite‐horizon, for the filtering error dynamics in the presence of saturated states, randomly occurring nonlinearities, and successive packet dropouts. By introducing a free matrix with its infinity norm less than or equal to 1, the error state is bounded by a convex hull so that some sufficient conditions obtained via solving a certain set of recursive nonlinear matrix inequalities. Furthermore, the obtained results are extended to the case when state saturations are partial. Two numerical simulation examples are provided to demonstrate the effectiveness and applicability of the proposed filter design approach. Copyright © 2012 John Wiley & Sons, Ltd.     

H ∞ filtering for discrete-time singular networked systems with communication delays and data missing

In this article, the problem of H _∞ filter design is investigated for discrete-time singular networked systems with both multiple stochastic time-varying communication delays and probabilistic missing measurements. Two kinds of stochastic time-varying communication delays, namely stochastic discrete delays and stochastic distributed delays, are simultaneously considered. The purpose of the addressed filtering problem is to design a filter such that, for the admissible random measurement missing and communication delays, the filtering error dynamics is asymptotically stable in the mean square with a prescribed H _∞ performance index. In terms of linear matrix inequality (LMI) method, a sufficient condition is established that ensures the asymptotical stability in the mean square with a prescribed H _∞ performance index of the filtering error dynamics and then the filter parameters are characterised by the solution to an LMI. A numerical example is introduced to demonstrate the effectiveness of the proposed design procedures.     

Observer-based H∞ fuzzy control for discrete-time Takagi–Sugeno fuzzy mixed delay systems with random packet losses and multiplicative noises

This paper investigates the observer-based H_∞ fuzzy control problem for a class of discrete-time fuzzy mixed delay systems with random communication packet losses and multiplicative noises, where the mixed delays comprise both discrete time-varying and distributed delays. The random packet losses are described by a Bernoulli distributed white sequence that obeys a conditional probability distribution, and the multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. In the presence of mixed delays, random packet losses and multiplicative noises, sufficient conditions for the existence of an observer-based fuzzy feedback controller are derived, such that the closed-loop control system is asymptotically mean-square stable and preserves a guaranteed H_∞ performance. Then a linear matrix inequality approach for designing such an observer-based H_∞ fuzzy controller is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results.     

Design of robust non‐fragile H∞ filters for uncertain neutral stochastic systems with distributed delays

This paper deals with the problem of robust non‐fragile H_∞ filtering for neutral stochastic systems with distributed delays and norm‐bounded parameter uncertainties. Attention is focused on the design of a filter which is subject to gain variations, such that the filtering error system is robustly stochastically stable with a prescribed H_∞ performance level for all admissible uncertainties. A delay‐dependent sufficient condition for the solvability of this problem is obtained in terms of a linear matrix inequality. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Bounded H∞ synchronization for time‐varying networks with probability‐dependent information

This paper addresses the bounded H_∞ synchronization problem for the time‐varying coupled networks with stochastic noises and randomly occurring nonlinearities over a finite horizon. The bounded H_∞ synchronization performance constraint is proposed to quantify the degree of the synchronization regarding the exogenous disturbances. The nonlinearities considered in this paper are assumed to satisfy the sector‐like conditions and characterized by a time‐varying Bernoulli distribution with measurable probability in real time. Based on the Kronecker product and the Hadamard product, a sufficient condition is established firstly to ensure the bounded H_∞ synchronization of the network by utilizing the probability‐dependent method. Then the obtained criterion is further converted into a computationally available one by transforming the time‐varying probability into a polytopic form, which is presented in terms of matrix inequalities and hence can be verified easily by applying the Matlab toolbox. Finally, simulation examples are given to demonstrate the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Delay-dependent reliable H ∞ filtering for sector-bounded nonlinear continuous-time systems with time-varying state delays and sensor failures

In this article, the reliable H _∞ filtering problem against sensor failures is investigated for a class of continuous-time systems with simultaneous sector-bounded nonlinearities and varying time delays. The focus of this article is on designing a reliable filter such that the filtering error system is asymptotically stable and meets the prescribed H _∞ norm constraint in the normal case as well as in the sensor failure case simultaneously. Linear matrix inequality conditions, which depend not only on the upper and lower bounds of delay but also on the upper bound of delay derivative, are obtained for the existence of admissible filters and, based on these, the filter design is cast into a convex optimisation problem. What is worth mentioning is that the information about the upper bound of the delay derivative is taken into consideration even if this upper bound is not smaller than 1. A numerical example is presented to illustrate the effectiveness and advantage of the developed filter design method.     

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     

Design of robust H ∞ filters for a class of uncertain nonlinear neutral stochastic systems with time delays

This article investigates the problem of robust H _∞ filtering for a class of nonlinear neutral stochastic time-delay systems with norm-bounded parameter uncertainties. The nonlinearities are assumed to satisfy the global Lipschitz conditions. By solving a set of certain linear matrix inequalities, an H _∞ filter is designed, which ensures both the robust stochastic stability and a prescribed H _∞ performance of the filtering error system for all admissible uncertainties. A numerical example is given to show the effectiveness of the design method proposed in this article.     

Robust H∞ filtering for a class of Markovian jump systems with time‐varying delays based on delta operator approach

In this paper, the robust H_∞ filtering problem for a class of discrete Markovian jump systems with time‐varying delays and linear fractional uncertainties is investigated based on delta operator approach. Based on Lyapunov‐Krasovskii functional in delta domain, new delay‐dependent sufficient conditions for the solvability of this problem are presented in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired jump H_∞ filter is given. The proposed method can unify some previous related continuous and discrete systems into the delta operator systems framework. Numerical examples are given to illustrate the effectiveness of the developed techniques. © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

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.     

Optimal‐switched extended H∞ filter for nonlinear systems with stochastic uncertainties

The extended H_∞ filter (EH_∞F) is a conservative solution with infinite‐horizon robustness for the state estimation problem regarding nonlinear systems with stochastic uncertainties, which leads to excessive costs in terms of filtering optimality and reduces the estimation precision, particularly when uncertainties related to external disturbances and noise appear intermittently. In order to restore the filtering optimality lost due to the conservativeness of the EH_∞F design, we developed an optimal‐switched (OS) filtering mechanism based on the standard EH_∞F to obtain an optimal‐switched extended H_∞ filter (OS‐EH_∞F). The OS mechanism has an error‐tolerant switched (ETS) structure, which switches the filtering mode between optimal and H_∞ robust by setting a switching threshold with redundancy to uncertainties, and a robustness‐optimality cost function (ROCF) is introduced to determine the threshold and optimize the ETS structure online. The ROCF is the weighted sum of the quantified filtering robustness and optimality. When a weight is given, the proposed OS‐EH_∞F can obtain the optimal state estimates while maintaining the filtering robustness at an invariant ratio. A simulation example of space target tracking has demonstrated the superior estimation performance of the OS‐EH_∞F compared with some other typical filters, thereby verifying the effectiveness of using the weight to evaluate the estimation result of the filters.     

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.