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.     

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 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.     

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.     

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.     

Delay‐dependent filtering design for time‐delay systems with Markovian jumping parameters

Two filtering problems—H_∞ filtering and H₂ filtering—for the linear Markovian jump systems with time delay are considered in this paper. The proposed new filtering approach guarantees that the results are less conservative than that obtained by other existing approaches. Numerical example well demonstrates the proposed algorithms. Copyright © 2006 John Wiley & Sons, Ltd.     

Neural‐network‐based finite‐time H∞ control for extended Markov jump nonlinear systems

This paper presents a neural‐network‐based finite‐time H_∞ control design technique for a class of extended Markov jump nonlinear systems. The considered stochastic character is described by a Markov process, but with only partially known transition jump rates. The sufficient conditions for the existence of the desired controller are derived in terms of linear matrix inequalities such that the closed‐loop system trajectory stays within a prescribed bound in a fixed time interval and has a guaranteed H_∞ noise attenuation performance for all admissible uncertainties and approximation errors of the neural networks. A numerical example is used to illustrate the effectiveness of the developed theoretic results. Copyright © 2009 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.     

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.     

Central suboptimal H∞ filter design for nonlinear polynomial systems

This paper presents the central finite‐dimensional H_∞ filter for nonlinear polynomial systems, which is suboptimal for a given threshold γ with respect to a modified Bolza–Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, the paper reduces the original H_∞ filtering problem to the corresponding optimal H₂ filtering problem, using the technique proposed in (IEEE Trans. Automat. Control 1989; 34 :831–847). The paper presents the central suboptimal H_∞ filter for the general case of nonlinear polynomial systems based on the optimal H₂ filter given in (Int. J. Robust Nonlinear Control 2006; 16 :287–298). The central suboptimal H_∞ filter is also derived in a closed finite‐dimensional form for third (and less) degree polynomial system states. Numerical simulations are conducted to verify performance of the designed central suboptimal filter for nonlinear polynomial systems against the central suboptimal H_∞ filter available for the corresponding linearized system. Copyright © 2008 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.     

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.     

Robust input‐output finite‐time filtering for uncertain Markovian jump nonlinear systems with partially known transition probabilities

In this paper, the robust input‐output finite‐time filtering problem is addressed for a class of uncertain Markovian jump nonlinear systems with partially known transition probabilities. Here, the disturbances, uncertainties, state delay, and distributed delays are all taken into account. Both the stochastic finite‐time boundedness and the stochastic input‐output finite‐time stability are introduced to the Markovian jump nonlinear systems with partially known transition probabilities. By constructing a reasonable stochastic Lyapunov functional and using linear matrix inequality techniques, sufficient conditions are established to guarantee the filtering error systems are stochastic finite‐time bounded and stochastic input‐output finite‐time stable, respectively. Finally, 2 examples are provided to illustrate the effectiveness of the proposed methods.     

Mode‐independent H∞ filtering for discrete‐time Markov jump linear system with parametric uncertainties and quantized measurements

This paper is concerned with the problem of H_∞ filtering for discrete‐time Markov jump linear system with parametric uncertainties and quantized measurements, when the jumping mode information is not accessible. By converting the quantized errors into a sector‐bounded nonlinearity, the parametric uncertainties and measurements quantization are dealt with in a unified framework. The mode‐independent H_∞ filter is designed, and sufficient conditions are established via Lyapunov function approach, such that for all possible uncertain parameters and quantization errors, the resulting filtering error system is robustly stochastically stable and achieves a guaranteed H_∞ filtering error performance index. A numerical example is provided to demonstrate the feasibility and effectiveness of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust H ∞ filtering for a class of uncertain stochastic hybrid neutral systems with time‐varying delay

This paper is devoted to the problem of robust H _∞ filtering for a class of uncertain switched neutral systems subject to stochastic disturbance and time‐varying delay. Attention is focused on the design of a full‐order switched filter such that the filtering error system is robust mean‐square exponentially stable with a prescribed weighted H _∞ performance. On the basis of the average dwell time approach and the piecewise Lyapunov function technique, sufficient conditions for the solvability of this problem are obtained in terms of linear matrix inequalities. Then, by solving the corresponding linear matrix inequalities, the desired full‐order switched filter is derived for all admissible uncertainties, time‐varying delay, and stochastic disturbances. A numerical example is given to illustrate the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust reliable dissipative filtering for Markovian jump nonlinear systems with uncertainties

This paper investigates the problem of robust reliable dissipative filtering for a class of Markovian jump nonlinear systems with uncertainties and time‐varying transition probability matrix described by a polytope. Our main attention is focused on the design of a reliable dissipative filter performance for the filtering error system such that the resulting error system is stochastically stable and strictly dissipative. By introducing a novel augmented Lyapunov–Krasovskii functional, a new set of sufficient conditions is obtained for the existence of reliable dissipative filter design in terms of linear matrix inequalities (LMIs). More precisely, a sufficient LMI condition is derived for reliable dissipative filtering that unifies the conditions for filtering with passivity and H_∞ performances. Moreover, the filter gains are characterized in terms of solution to a set of linear matrix inequalities. Finally, two numerical examples are provided to demonstrate the effectiveness and potential of the proposed design technique. Copyright © 2016 John Wiley & Sons, Ltd.     

Distributed H2/H∞ filtering over infinite horizon

This paper studies distributed H₂/H_∞ filtering problem with the aid of neighbors’ information. It is assumed that there are both bounded power uncertainty and stochastic white noise in the model of the considered system. A 2‐step design approach is proposed to calculate the observer gain and the coupling gain in the proposed observers. In order to reduce the computation load of solving coupled matrix equations, a simplified design procedure is also proposed. Simulation of 2 examples shows the effectiveness of the proposed filter design procedure.     

Composite adaptive anti‐disturbance resilient control for Markovian jump systems with partly known transition rate and multiple disturbances

In this paper, the problem of composite adaptive anti‐disturbance resilient control is investigated for Markovian jump systems with partly known transition rate and multiple disturbances. The considered multiple disturbances include two types: one is external disturbance, while the other is an unexpected nonlinear signal which is described as a nonlinear function. Composite adaptive disturbance observers are constructed to estimate these disturbances, and the estimations are applied to feedforward compensation. Then a composite adaptive anti‐disturbance resilient controller is obtained. Furthermore, some sufficient conditions are presented in terms of linear matrix inequalities such that the closed‐loop system is stochastically stable with performance. Finally, a numerical example and an application example are given to illustrate the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.