H∞ filtering for singular systems with time‐varying delay

This paper is concerned with the delay‐dependent H_∞ filtering problem for singular systems with time‐varying delay in a range. In terms of linear matrix inequality approach, the delay‐range‐dependent bounded real lemmas are proposed, which guarantee the considered system to be regular, impulse free and exponentially stable while satisfying a prescribed H_∞ performance level. The sufficient conditions are proposed for the existence of linear H_∞ filter. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed methods. 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.     

Resilient filtering for cyber‐physical systems under denial‐of‐service attacks

Owing to the deep integration of control, computation, and communication, cyber‐physical systems (CPSs) play an important role in wide real‐world applications. In this paper, we investigate the problem of resilient filter design of CPSs under malicious denial‐of‐service (DoS) attacks launched by adversaries. Firstly, based on two standard assumptions concerning with the frequency and duration of DoS attacks, we state the H_∞ filtering problem for the CPSs under DoS attacks. Then, sufficient conditions are developed to ensure that, when there are DoS attacks, the filtering error dynamics of the underlying CPSs is mean square exponential stable with a prescribed H_∞ disturbance attenuation performance. Furthermore, a switched filter is designed for CPSs under DoS attacks. Examples are given to illustrate the effectiveness and potential of the proposed new design techniques.     

H∞ finite‐horizon filtering for complex networks with state saturations: The weighted try‐once‐discard protocol

This paper addresses the finite‐horizon H_∞ filtering problem for a kind of discrete state‐saturated time‐varying complex networks subjected to the weighted try‐once‐discard (WTOD) protocol. Under the WTOD protocol, only the measurement signal from one sensor node is allowed to be transmitted to the filter at each time point, where such a node is selected based on a certain quadratic selection principle. The main purpose of this paper is to design an H_∞ filter that guarantees the disturbance attenuation level on a given finite time‐horizon for the underlying complex network subject to both state saturations and WTOD protocols. By using the convex hull approach, sufficient conditions are first obtained to ensure the existence for the desired filter to achieve the H_∞ performance specification by means of a few recursive matrix inequalities. Then, based on the obtained results, the filter parameters are designed, which cope effectively with both state saturations and communication protocols. Finally, a numerical simulation is employed to demonstrate the validity of the developed filter algorithm.     

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.     

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.     

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.     

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.     

Nonfragile H∞ filtering for discrete multirate time‐delayed systems over sensor networks characterized by Gilbert‐Elliott models

In this article, the nonfragile H_∞ filtering problem is investigated for a class of discrete multirate time‐delayed systems over sensor networks. The probabilistic packet dropout occurs during the information transmissions among the sensor nodes in the sensor network characterized by the Gilbert‐Elliott model. In order to take the multirate sampling into account, the state updating period of the system and the sampling period of the sensors are allowed to be different. The variation of the filter gain is considered to reflect the physical errors with the filter implementation. The aim of this article is to design a set of nonfragile filters such that, in the presence of multirate sampling, time‐delays, and packet dropouts, the filtering error dynamics is exponentially mean‐square stable and also satisfies the H_∞ performance requirement. By using the Lyapunov‐Krasovskii functional approach, a sufficient condition is derived, which ensures the exponential mean‐square stability and the H_∞ performance requirement of the filtering error dynamics. Then, the filter gains are characterized in terms of the solution to a set of matrix inequalities. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed filtering scheme.     

Asynchronous H∞ filtering for time delayed APF with MDADT based on T‐S fuzzy model

This paper investigates the H_∞ asynchronous filtering problem for active power filter (APF) systems with time delayed to monitor the states of these systems. APF system is represented by T‐S fuzzy model. The phenomenon of asynchronous often appears in the practical system. And in this paper, asynchronous means that the switching of the filters we designed has a lag to the switching of the system models. By using the MDADT and the Lyapunov‐Krasovskii function methods, the switching filtering error system is delay‐dependent stability and has the H_∞ performance. The filter parameter is solved by linear matrix inequalities (LMIs). A simulation example is given to show the efficiency of the proposed methods.     

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.     

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.     

Reliable H ∞ Filtering for Mixed Time‐Delay Systems with Stochastic Nonlinearities and Multiplicative Noises

This paper investigates the reliable H_∞ filtering problem for a class of mixed time‐delay systems with stochastic nonlinearities and multiplicative noises. The mixed delays comprise both discrete time‐varying and distributed delays. The stochastic nonlinearities in the form of statistical means cover several well‐studied nonlinear functions. 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. In the presence of mixed delays, stochastic nonlinearities, and multiplicative noises, sufficient conditions for the existence of a reliable H _∞ filter are derived, such that the filtering error dynamics is asymptotically mean‐square stable and also achieves a guaranteed H _∞ performance level. Then, a linear matrix inequality (LMI) approach for designing such a reliable H _∞ filter is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results.     

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.     

A less conservative method for designing H∞ filters for linear time‐delay systems

This paper focuses on H_∞ filtering for linear time‐delay systems. A new Lyapunov–Krasovskii functional (LKF) is constructed by uniformly dividing the delay interval into two subintervals, and choosing different Lyapunov matrices on each subinterval. Based on this new LKF, a less conservative delay‐dependent bounded real lemma (BRL) is established to ensure that the resulting filtering error system is asymptotically stable with a prescribed H_∞ performance. Then, this new BRL is equivalently converted into a set of linear matrix inequalities, which guarantee the existence of a suitable H_∞ filter. Compared with some existing filtering results, some imposed constraints on the Lyapunov matrices are removed through derivation of the sufficient condition for the existence of the filter. Numerical examples show that the results obtained in this paper significantly improve the H_∞ performance of the filtering error system over some existing results in the literature. Copyright © 2008 John Wiley & Sons, Ltd.     

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     

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.     

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.     

Further results on H∞ filtering for discrete‐time systems with state delay

This article studies the problem of H_∞ filtering for linear discrete‐time systems with state delay. Via delay partitioning idea, two new H_∞ filter design methods are proposed with much less conservatism than most existing results. The improvement lies in constructing two new Lyapunov–Krasovskii functionals by partitioning the known constant lower bound of delay into several segments equally. Using free‐weighting matrix and Jensen inequality methods, two new delay‐dependent bound real lemmas (BRLs) are obtained, which depend on both the delay and the partitioning number. Based on the obtained BRLs, new H_∞ filter design approaches are proposed in terms of linear matrix inequalities. The results are immediately extended to multiple time delay case and polytopic uncertain case, respectively. Three numerical examples are presented to illustrate the effectiveness and advantage of the proposed approaches. Copyright © 2010 John Wiley & Sons, Ltd.     

H∞ Filtering for Spatially Interconnected Time‐Delay Systems with Interconnected Chains in Finite Frequency Domains

This paper deals with the problem of delay‐dependent H_∞ filtering for spatially interconnected time‐delay systems (SITSs) with interconnected chains in finite frequency domains. First, a multidimensional (N‐D) hybrid time‐delay Roesser model and a delay‐dependent finite frequency bounded ream lemma (BRL) for SITSs with interconnected chains are proposed. Then, using the obtained delay‐dependent finite frequency BRL, a finite frequency H_∞ filter design method can be derived by solving a set of linear matrix inequalities (LMIs). Finally, a practical example is provided to clearly demonstrate the effectiveness of the proposed method.