Fault detection for discrete‐time switched singular time‐delay systems: an average dwell time approach

In this paper, the fault detection problem is investigated for a class of discrete‐time switched singular systems with time‐varying state delays. The residual generator is firstly constructed based on a switched filter, and the design of fault detection filter is formulated as an H _∞ filtering problem, that is, minimizing the error between residual and fault in the H _∞ sense. Then, by constructing an appropriate decay‐rate‐dependent piecewise Lyapunov function and using the average dwell time scheme, a sufficient condition for the residual system to be regular, causal, and exponential stable while satisfying a prescribed H _∞ performance is derived in terms of linear matrix inequalities (LMIs). The corresponding solvability condition for the desired fault detection filters is also established via LMI approach. Finally, a numerical example is presented to show the effectiveness of the developed theoretical results.Copyright © 2012 John Wiley & Sons, Ltd.     

Finite‐time H ∞ filtering for a class of discrete‐time Markovian jump systems with partly unknown transition probabilities

This paper is concerned with the problem of finite‐time H _∞ filtering for a class of Markovian jump systems subject to partial information on the transition probabilities. By introducing some slack matrix variables in terms of probability identity, a less conservative bounded real lemma is derived to ensure that filtering Markovian jump systems is finite‐time stable. Finally, the existence criterion of the desired filter is obtained such that the corresponding filtering error system is finite‐time bounded with a guaranteed H _∞ performance index. An example is given to illustrate the efficiency of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Exponential l2 − l∞ filtering for discrete‐time switched systems under a new framework

In this paper, a robust exponential l₂ ? l_∞ filtering problem is addressed for discrete‐time switched systems with polytopic uncertainties. The purpose of robust exponential l₂ ? l_∞ filtering is to design a filter such that the resulting filtering error system is robustly exponentially stable with a decay rate and a prescribed exponential l₂ ? l_∞ performance index. The robust exponential l₂ ? l_∞ filtering problem is solved via an average dwell time approach. Sufficient conditions in terms of strict LMI are derived for checking the robust exponential stability of a filter. An explicit expression for the desired robust exponential filter is also given. Finally, a numerical example is provided to demonstrate the potential and effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust H∞ filtering for switched linear discrete‐time systems with polytopic uncertainties

In this paper, the problem of robust H_∞ filtering for switched linear discrete‐time systems with polytopic uncertainties is investigated. Based on the mode‐switching idea and parameter‐dependent stability result, a robust switched linear filter is designed such that the corresponding filtering error system achieves robust asymptotic stability and guarantees a prescribed H_∞ performance index for all admissible uncertainties. The existence condition of such filter is derived and formulated in terms of a set of linear matrix inequalities (LMIs) by the introduction of slack variables to eliminate the cross coupling of system matrices and Lyapunov matrices among different subsystems. The desired filter can be constructed by solving the corresponding convex optimization problem, which also provides an optimal H_∞ noise‐attenuation level bound for the resultant filtering error system. A numerical example is given to show the effectiveness and the potential of the proposed techniques. Copyright © 2006 John Wiley & Sons, Ltd.     

On robust H∞ filtering of uncertain Markovian jump time‐delay systems

This paper is concerned with the problems of stability analysis, H_∞ performance analysis, and robust H_∞ filter design for uncertain Markovian jump linear systems with time‐varying delays. The purpose is to improve the existing results on these problems. Firstly, a new delay‐dependent stability criterion is obtained on the basis of a novel mode‐dependent Lyapunov functional. Secondly, a new delay‐dependent bounded real lemma (BRL) is derived. It is shown that the presented stability criterion and the BRL are less conservative than the existing ones in the literature. Thirdly, with the new BRL, delay‐dependent conditions for the solvability of the addressed H_∞ filtering problem are given. All the results obtained in this paper are expressed by means of strict linear matrix inequalities. Three numerical examples are provided to demonstrate the utility of the proposed methods. Copyright © 2011 John Wiley & Sons, Ltd.     

Delay‐dependent robust L2–L∞ filtering of T‐S fuzzy systems with time‐varying delays

This paper considers the problem of robust delay‐dependent L₂–L_∞ filtering for a class of Takagi–Sugeno fuzzy systems with time‐varying delays. The purpose is to design a fuzzy filter such that both the robust stability and a prescribed L₂–L_∞ performance level of the filtering error system are guaranteed. A delay‐dependent sufficient condition for the solvability of the problem is obtained and a linear matrix inequality (LMI) approach is developed. A desired filter can be constructed by solving a set of LMIs. Copyright © 2009 John Wiley & Sons, Ltd.     

Fault detection for a class of network‐based nonlinear systems with communication constraints and random packet dropouts

This paper is dealt with the fault detection (FD) problem for a class of network‐based nonlinear systems with communication constraints and random packet dropouts. The plant is described by a Takagi–Sugeno fuzzy time‐delay model, it has multiple sensors and only one of them is actually communicated with the FD filter at each transmission instant, and the packet dropouts occur randomly. The goal is to design a FD filter such that, for all unknown inputs, control inputs, time delays and incomplete data conditions, the estimation error between the residual and ‘fault’ (or, more generally, the weighted fault) is minimized. By casting the addressed FD problem into an auxiliary H_∞ filtering problem of a stochastic switched fuzzy time‐delay system, a sufficient condition for the existence of the desired FD filter is established in terms of linear matrix inequalities. A numerical example is provided to illustrate the effectiveness and applicability of the proposed technique. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust weighted H∞ filtering for networked systems with intermittent measurements of multiple sensors

In this paper, we investigate the robust weighted H_∞ filtering problem for networked systems with intermittent measurements under the discrete‐time framework. Multiple outputs of the plant are measured by separate sensors, each of which has a specific failure rate. Network‐induced delay, packet dropouts and network‐induced disorder phenomena are all incorporated in the modeling of the network link. The resulting closed‐loop system involves both delayed noise and non‐delayed noise. In order to make full use of the delayed information, we define a weighted H_∞ performance index. Sufficient delay‐dependent and parameter‐dependent conditions for the existence of the filter and the solvability of the addressed problem are given via a set of linear matrix inequalities. Two simulation examples are presented to illustrate the relationship between the minimal performance level and the weighting factor, which show the effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

H∞ filtering for continuous‐time singular systems with time‐varying delay

This paper focuses on H_∞ filter design for continuous‐time singular systems with time‐varying delay. A delay‐dependent H_∞ performance analysis result is first established for error systems via a novel estimation method. By combining a well‐known inequality with a delay partition technique, the upper bound of the derivative of the Lyapunov functional is estimated more tightly and expressed as a convex combination with respect to the reciprocal of the delay rather than the delay. Based on the derived H_∞ performance analysis results, a regular and impulse‐free H_∞ filter is designed in terms of linear matrix inequalities (LMIs). A numerical example is given to demonstrate the merits of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust H∞ filtering for uncertain Markovian jump systems with mode‐dependent distributed delays

This paper deals with the problem of robust H_∞ filter design for Markovian jump systems with norm‐bounded time‐varying parameter uncertainties and mode‐dependent distributed delays. Both the state and the measurement equations are assumed to be with distributed delays. Sufficient conditions for the existence of robust H_∞ filters are obtained. Via solving a set of linear matrix inequalities, a desired filter can be constructed. The developed theory is illustrated by a simulation example. Copyright © 2009 John Wiley & Sons, Ltd.     

Delay‐dependent H∞ performance analysis and filtering for Markovian jump systems with interval time‐varying delays

This paper investigates the problems of H_∞ disturbance attenuation and H_∞ filtering for Markovian jump systems with interval time‐varying delays. In terms of linear matrix inequalities, a less conservative delay‐range‐dependent H_∞ performance condition for Markovian jump systems is proposed by constructing a different Lyapunov–Krasovskii functional. The resulting criterion has advantages over some previous ones in that they involve fewer matrix variables, but has less conservatism. Based on this new condition, an improved H_∞ filtering algorithm is developed. Numerical examples are provided to demonstrate the efficiency and reduced conservatism of the results in this paper. Copyright © 2009 John Wiley & Sons, Ltd.     

Fault detection for nonlinear networked systems with random packet dropout and probabilistic interval delay

In this paper, the fault detection (FD) problem of nonlinear networked control systems (NCSs) is investigated. A nonlinear stochastic systems model is proposed to account for the NCSs with network‐induced random packet dropout and non‐uniformly distributed time‐varying delay in both from sensor to controller and from controller to actuator. On the basis of the new model, by employing FD filter as residual generator, the addressed FD problem is converted into auxiliary nonlinear H _∞ filtering problem. Then, with the help of Lyapunov functional approach, a sufficient condition for the desired FD filter is constructed in terms of certain linear matrix inequalities, which depends on not only nonlinear level but also delay interval occurrence rate and successful joint packet transmission rate. Especially, a trade‐off phenomenon among maximum allowable delay bound, nonlinear level, and successful joint packet transmission rate is found, which typically resulted from the limited bandwidth of the communication networks. The effectiveness of the proposed methods is demonstrated by simulation examples. Copyright © 2011 John Wiley & Sons, Ltd.     

Reliable H∞ filtering for discrete time‐delay Markovian jump systems with partly unknown transition probabilities

In this paper, the reliable H_∞ filtering problem is studied for a class of discrete nonlinear Markovian jump systems with sensor failures and time delays. The transition probabilities of the jumping process are assumed to be partly unknown. The failures of sensors are quantified by a variable taking values in a given interval. The time‐varying delay is unknown with given lower and upper bounds. The purpose of the addressed reliable H_∞ filtering problem is to design a mode‐dependent filter such that the filtering error dynamics is asymptotically mean‐square stable and also achieves a prescribed H_∞ performance level. By using a new Lyapunov–Krasovskii functional and delay‐partitioning technique, sufficient delay‐dependent conditions for the existence of such a filter are obtained. The filter gains are characterized in terms of the solution to a convex optimization problem that can be easily solved by using the semi‐definite programme method. A numerical example is provided to demonstrate the effectiveness of the proposed design approach. Copyright © 2011 John Wiley & Sons, Ltd.     

Observer design for nonlinear parameter‐varying systems: Application to diesel engines

This paper deals with the problem of designing a nonlinear observer for diesel engines. The goal is to estimate the masses entering the cylinders and the inlet and exhaust pressures. To achieve this, the considered model subject to disturbances contains linear parameter‐varying part and nonlinear part having a large Lipschitz constant. The H _∞ criterion is used to reject the disturbances. Besides, the modified mean value theorem is applied to express the nonlinear error dynamics as a convex combination of known matrices with time‐varying coefficients. The sufficient conditions are derived and given in terms of linear matrix inequality. The advantage of the proposed method is that it can be applied to a wider class of nonlinear systems, particulary our case: diesel engines. The proposed approach is tested and evaluated using an advanced diesel engine professional simulator AMEsim (LMS International, Leuven, Belgium). Copyright © 2014 John Wiley & Sons, Ltd.     

Delay‐dependent model reduction for continuous‐time switched state‐delayed systems

This paper studies the problem of exponential H_∞ model reduction for continuous‐time switched delay system under average dwell time (ADT) switching signals. Time delay under consideration is interval time varying. Our attention is focused on the construction of the desired reduced order models, which guarantee that the resulting error systems under ADT switching signals are exponentially stable with an H_∞ norm bound. By introducing a block matrix and making use of the ADT approach, delay‐dependent sufficient conditions for the existence of reduced order models are derived and formulated in terms of strict linear matrix inequalities (LMIs). Owing to the absence of non‐convex constraints, it is tractable to construct an admissible reduced order model. The effectiveness of the proposed methods is illustrated via two numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive robust H∞ state feedback control for linear uncertain systems with time‐varying delay

This paper considers the problem of adaptive robust H_∞ state feedback control for linear uncertain systems with time‐varying delay. The uncertainties are assumed to be time varying, unknown, but bounded. A new adaptive robust H_∞ controller is presented, whose gains are updating automatically according to the online estimates of uncertain parameters. By combining an indirect adaptive control method and a linear matrix inequality method, sufficient conditions with less conservativeness than those of the corresponding controller with fixed gains are given to guarantee robust asymptotic stability and H_∞ performance of the closed‐loop systems. A numerical example and its simulation results are given to demonstrate the effectiveness and the benefits of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

Quantized H∞ filtering for state‐delayed systems with finite frequency specifications

This paper presents a novel design approach for the finite frequency (FF) H_∞ filtering problem for discrete‐time state‐delayed systems with quantized measurements. The system state and output are assumed affected by FF external noises. Attention is focused on the design of a stable filter that guarantees the stability and a prescribed ?₂ gain performance level for the filtering error system in the FF domain of input noises. Sufficient conditions for the solvability of this problem are developed by choosing an appropriate Lyapunov‐Krasovskii functional based on the delay partitioning technique and using the FF ?₂ gain definition combined with the generalized S‐procedure. Then, by means of Finsler's lemma, the derived conditions are linearized and additional slack variables are further introduced to more flexible result. Final filter design conditions are consequently established in terms of linear matrix inequalities in three different frequency ranges, ie, low‐, middle‐ and high‐frequency range. Finally, a simulation example is presented to illustrate the effectiveness and the merits of the proposed approach.     

Average consensus with weighting matrix design for quantized communication on directed switching graphs

We study average consensus for directed graphs with quantized communication under fixed and switching topologies. In the presence of quantization errors, conventional consensus algorithms fail to converge and may suffer from an unbounded asymptotic mean square error. We develop robust consensus algorithms to reduce the effect of quantization. Specifically, we introduce a robust weighting matrix design and use the H _∞ performance index to measure the sensitivity from the quantization error to the consensus deviation. Linear matrix inequalities are used as design tools. The mean square deviation is proven to converge and its upper bound is explicitly given in the case of fixed topology with probabilistic quantization. Numerical results demonstrate the effectiveness of this method. Copyright © 2012 John Wiley & Sons, Ltd.