Finite‐horizon fault estimation for time‐varying systems with multiple fading measurements under torus‐event–based protocols

In this paper, the issue of the finite‐horizon H_∞ fault estimation is dealt with for a class of discrete time‐varying systems subject to randomly occurring faults and multiple fading measurements. The missing phenomena may occur in a random way from different sensors, which is represented by an individual stochastic variable meeting a certain probability distribution. Furthermore, in order to alleviate the communication burden, the torus‐event–based protocols are adopted to schedule the data transmissions only when some significant events occur. Our aim of the presented issue is to estimate the fault such that, with multiple fading measurements via the received information governed by torus‐event–based protocols, the H_∞ index is satisfied over a given finite horizon. Sufficient conditions are obtained for the desired time‐varying estimator in terms of the technique of stochastic analysis and the methods of completing squares. The desired estimator gains are calculated by working out two backward recursive Riccati difference equations. Finally, a numerical simulation is given to verify the usefulness of our designed fault estimation approach.     

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.     

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∞ 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.     

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.     

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.     

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.     

Robust mixed H2/H∞ delayed state feedback control of uncertain neutral systems with time‐varying delays

This paper considers the problem of robust mixed H₂/H_∞ delayed state feedback control for a class of uncertain neutral systems with time‐varying discrete and distributed delays. Based on the Lyapunov–Krasovskii functional theory, new required sufficient conditions are established in terms of delay‐range‐dependent linear matrix inequalities for the stability and stabilization of the considered system using some free matrices. The desired robust mixed H₂/H_∞ delayed state feedback control is derived based on a convex optimization method such that the resulting closed‐loop system is asymptotically stable and satisfies H₂ performance with a guaranteed cost and a prescribed level of H_∞ performance, simultaneously. Finally, a numerical example is given to illustrate the effectiveness of our approach. Copyright © 2008 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.     

H∞ fault estimation with randomly occurring uncertainties,quantization effects and successive packet dropouts: The finite‐horizon case

In this paper, the finite‐horizon H_∞ fault estimation problem is investigated for a class of uncertain nonlinear time‐varying systems subject to multiple stochastic delays. The randomly occurring uncertainties (ROUs) enter into the system due to the random fluctuations of network conditions. The measured output is quantized by a logarithmic quantizer before being transmitted to the fault estimator. Also, successive packet dropouts (SPDs) happen when the quantized signals are transmitted through an unreliable network medium. Three mutually independent sets of Bernoulli‐distributed white sequences are introduced to govern the multiple stochastic delays, ROUs and SPDs. By employing the stochastic analysis approach, some sufficient conditions are established for the desired finite‐horizon fault estimator to achieve the specified H_∞ performance. The time‐varying parameters of the fault estimator are obtained by solving a set of recursive linear matrix inequalities. Finally, an illustrative numerical example is provided to show the effectiveness of the proposed fault estimation approach. Copyright © 2014 John Wiley & Sons, Ltd.     

H∞ output tracking control for uncertain networked control systems via a switched system approach

In this paper, the problem of H_∞ output tracking control for networked control systems with random time delays and system uncertainties is investigated. Effective sampling instant that is tightly related with transmission delay from sensor to actuator is proposed to ensure that the random variable time delay is always shorter than one effective sampling period. By using both active time‐varying sampling period strategy and hybrid node‐driven mechanism, the switching instant is coincided with the effective sampling instant. An augmented time‐varying networked tracking system model is provided by including the output tracking error as an additional state. However, random transmission delay causes indeterminate sampling period, which induces infinite subsystems. Gridding approach is introduced to transform the continuous time axis into discrete‐time sequences, which guarantees the finite number of switching rules. By employing multiple Lyapunov–Krasovskii functions, linear matrix inequality (LMI)‐based output tracking H_∞ performance analysis is presented, and robust switching H_∞ model reference tracking controller for networked control systems with communication constraints and system uncertainties is designed to guarantee asymptotic tracking of prescribed reference outputs while rejecting disturbances. Finally, simulation results illustrate the correctness and effectiveness of the proposed approaches. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Robust H ∞ filtering for networked systems with multiple state delays

In this paper, a new robust H _∞ filter design problem is studied for a class of networked systems with multiple state-delays. Two kinds of incomplete measurements, namely, measurements with random delays and measurements with stochastic missing phenomenon, are simultaneously considered. Such incomplete measurements are induced by the limited bandwidth of communication networks, and are modelled as a linear function of a certain set of indicator functions that depend on the same stochastic variable. Attention is focused on the analysis and design problems of a full-order robust H _∞ filter such that, for all admissible parameter uncertainties and all possible incomplete measurements, the filtering error dynamics is exponentially mean-square stable and a prescribed H _∞ attenuation level is guaranteed. Some recently reported methodologies, such as delay-dependent and parameter-dependent stability analysis approaches, are employed to obtain less conservative results. Sufficient conditions, which are dependent on the occurrence probability of both the random sensor delay and missing measurement, are established for the existence of the desired filters in terms of certain linear matrix inequalities (LMIs). When these LMIs are feasible, the explicit expression of the desired filter can also be characterized. Finally, numerical examples are given to illustrate the effectiveness and applicability of the proposed design method.     

H∞ filtering for discrete-time systems with randomly varying sensor delays

This paper investigates an H_∞ filtering problem for discrete-time systems with randomly varying sensor delays. The stochastic variable involved is a Bernoulli distributed white sequence appearing in measured outputs. This measurement mode can be used to characterize the effect of communication delays and/or data-loss in information transmissions across limited bandwidth communication channels over a wide area. H_∞ filtering of this class of systems is used to design a filter using the measurements with random delays to ensure the mean-square stochastic stability of the filtering error system and to guarantee a prescribed H_∞ filtering performance. A sufficient condition for the existence of such a filter is presented in terms of the feasibility of a linear matrix inequality (LMI). Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.     

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.     

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.     

Finite‐horizon fault estimation under imperfect measurements and stochastic communication protocol: Dealing with finite‐time boundedness

In this paper, we analyze the finite‐horizon fault estimation issue for a kind of time‐varying nonlinear systems with imperfect measurement signals under the stochastic communication protocol (SCP). The imperfect measurements result from randomly occurring sensor nonlinearities obeying sensor‐wise Bernoulli distributions. The Markov‐chain‐driven SCP is introduced to regulate the signal transmission to alleviate the communication congestion. The aim of the considered issue is to propose the design algorithm of a group of time‐varying fault estimators such that the estimation error dynamics satisfies both the H_∞ and the finite‐time boundedness (FTB) performance requirements. First, sufficient conditions are set up to guarantee the existence of the satisfactory H_∞ FTB fault estimators through intensive stochastic analyses and matrix operations. Then, the gains of such fault estimators are explicitly parameterized by resorting to the solution to recursive linear matrix inequalities. Finally, the correctness of the devised fault estimation approach is demonstrated by a numerical example.     

Time‐varying filter design for semi‐Markov jump linear systems with intermittent transmission

This paper focuses on the filter design problem for semi‐Markov jump linear systems. The system outputs are transmitted to the filter via networks, and it is assumed that the transmission is imperfect with data packet dropouts subject to the Bernoulli random binary distribution. A σ‐error mean square stability criterion is first derived for the underlying systems. On the basis of the criterion, the H_∞ performance analysis is conducted. By constructing a time‐varying Lyapunov function, a time‐varying H_∞ filter scheme is investigated. Because the presented approach can cover the mode‐dependent and mode‐independent time‐invariant H_∞ filter schemes as special cases, the conservatism of the derived results is less than those of the time‐invariant filter schemes. An active suspension system with activator uncertainties is lastly presented to illustrate the effectiveness and feasibility of the derived theoretical results. Copyright © 2017 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.     

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.