ℋ︁∞ and l2–l∞ filtering for two‐dimensional linear parameter‐varying systems

In this paper, the ??_∞ and l₂–l_∞ filtering problem is investigated for two‐dimensional (2‐D) discrete‐time linear parameter‐varying (LPV) systems. Based on the well‐known Fornasini–Marchesini local state‐space (FMLSS) model, the mathematical model of 2‐D systems under consideration is established by incorporating the parameter‐varying phenomenon. The purpose of the problem addressed is to design full‐order ??_∞ and l₂–l_∞ filters such that the filtering error dynamics is asymptotic stable and the prescribed noise attenuation levels in ??_∞ and l₂–l_∞ senses can be achieved, respectively. Sufficient conditions are derived for existence of such filters in terms of parameterized linear matrix inequalities (PLMIs), and the corresponding filter synthesis problem is then transformed into a convex optimization problem that can be efficiently solved by using standard software packages. A simulation example is exploited to demonstrate the usefulness and effectiveness of the proposed design method. Copyright © 2007 John Wiley & Sons, Ltd.     

Extended dissipative filtering of fuzzy systems with time-varying delay under imperfect premise matching

This paper investigates the extended dissipative filter design problems for continuous-time fuzzy systems with time-varying delays under imperfect premise variables based on a unified performance index?extended dissipative. Attention is focused on solving the H_∞, L₂ ? L_∞, passive and dissipative filtering problems for fuzzy systems with time-varying delays under this unified framework. Based on the unified performance index, a new delay-dependent filter design approach in terms of linear matrix inequalities is obtained by employing Lyapunov–Krasovskii functional method together with a novel efficient integral inequality. The designed filter can guarantee the filtering error system satisfy the prescribed H_∞, L₂ ? L_∞, passive and dissipative performance by tuning the weighting matrices in the conditions. Moreover, in this paper, the fuzzy filter does not need to share the same membership function with fuzzy model, which can enhance design flexibility and robust property of the fuzzy filter system. Finally, two examples are provided to illustrate the effectiveness and significant improvement of the method proposed in this paper.     

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.     

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.     

L2–L∞ filtering for nonlinear stochastic systems

A sufficient condition for a general nonlinear stochastic system to have L₂?L_∞ gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton–Jacobi inequality (HJI). Based on this criterion, the existence of an L₂?L_∞ filter is given by a second‐order nonlinear HJI, and the filter matrices can be obtained by solving such an HJI. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

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.     

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.     

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.     

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.     

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.     

Optimal H∞ scaling for sensitivity optimization of detection filters

The paper deals with the sensitivity optimization of detection filters in linear time‐varying (LTV) systems which are subject to multiple simultaneous faults and disturbances. The robust fault detection filter design problem as a scaled H_∞ filtering problem is considered. The effect of two different input scaling approaches to the optimization process is investigated. The objective is to provide the smallest scaled L₂ gain of the unknown input of the system that is guaranteed to be less than a prespecified level, i.e., to produce a filter with optimal disturbance suppression capability in such a way that sufficient sensitivity to failure modes should still be maintained. It is shown how to obtain bounds on the scaled L₂ gain by transforming the standard H_∞ filtering problem into a convex feasibility problem, specifically, a structured, linear matrix inequality (LMI). Numerical examples demonstrating the effect of the scaled optimization with respect to conventional H_∞ filtering is presented. Copyright © 2002 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     

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     

L∞ Observer for Uncertain Linear Systems

In this paper, an L_∞ observer design method is proposed for linear system subject to parameter uncertainty and bounded disturbance. The proposed L_∞ observer, which satisfies a peak‐to‐peak disturbances attenuation performance, is designed to overbound the estimation error. Moreover, sufficient conditions for the design of L_∞ observer are derived and expressed in terms of linear matrix inequalities (LMIs). The novelty of the proposed method is that we develop an L_∞ observer that not only can attenuate bounded disturbance but also provides an upper bound of estimation error norm. Simulation results are presented to illustrate the effectiveness of the proposed method.     

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.     

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.     

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.     

Improved L 2–L ∞ filtering for stochastic time-delay systems

The L ₂–L _∞ filtering problem for continuous-time polytopic uncertain stochastic time-delay systems is investigated. The main purpose is to design a full-order filter guaranteeing a prescribed L ₂–L _∞ attenuation level for the filtering error system. A simple alternative proof is given for an enhanced LMI (linear matrix inequality) representation of L ₂–L _∞ performance. Based on the criterion which keeps Lyapunov matrices out of the products of system dynamic matrices, a sufficient condition for the existence of a robust estimator is formulated in terms of LMIs. The corresponding filter design is cast into a convex optimization problem. A numerical example is employed to demonstrate the feasibility and advantage of the proposed design.     

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.     

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.