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.     

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.     

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.     

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.     

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.     

H∞ filtering of discrete-time switched singular systems with time-varying delays

In this article, the analysis and design problems of H_∞ filtering for a class of discrete-time switched singular systems with time-varying delay under an arbitrary switching signal are investigated. The main attention is focused on the design of a linear mode-dependent filter guaranteeing the regularity, causality, and asymptotic stability of the resulting filtering error system with a prescribed H_∞ performance bound. By using a multiple Lyapunov-Krasovskii functional, and utilizing the linearization technique, novel sufficient conditions for the solvability of H_∞ problem are derived in terms of linear matrix inequalities. Solving that, the desired filter gains can be determined. Any model transformation of system, which often leads the large computational burden is involved. The free weighting matrix technique is introduced to provide additional degree of freedom, which improves the conservativeness of the developed method. Finally, numerical examples are given to demonstrate the effectiveness and the merit of the proposed approach and to compare the obtained results with some previous works in the literature.     

Teaching sampled‐data H∞ control theory using arm robot experiment system

This paper explains how to use an arm robot experiment system to teach sampled‐data H_∞ control theory. A design procedure is presented for a digital tracking control system for a continuous plant with structured uncertainties; the target is the positioning control of an arm robot. To guarantee the robust stability of the closed‐loop system and provide the desired closed‐loop performance, the design problem is first formulated as a sampled‐data H_∞ control problem, and is then transformed into an equivalent discrete‐time H_∞ control problem. Finally, linear matrix inequalities are used to obtain a reduced‐order output‐feedback controller and a static state‐feedback controller. In a course, the design procedure is explained and practice is provided through simulations and experiments. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

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.     

Sampled-data filter design for large-scale interconnected systems with sensor fault and missing measurements

This article focuses on a decentralized sampled-data filter design for a class of large-scale interconnected systems. Precisely in the addressed system, the inevitable factors such as missing measurements, time-varying delays, randomly occurring uncertainties, and impulsive effects are taken into consideration. Also, we incorporated the gain perturbations and sensor faults in the proposed filter design. Furthermore, a new set of sufficient criterion has been derived by choosing an appropriate Lyapunov-Krasovskii functional that ensures the asymptotic stability of the resulting augmented filtering error system with the prescribed mixed H_∞ and passive performance index. Specifically, the corresponding filter gain matrices are derived by solving the developed sufficient criterion formulated in terms of linear matrix inequalities. The effectiveness of the proposed filter design technique are then exemplified by two numerical examples with simulations.     

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.     

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.     

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.     

Robust learning controller design for MIMO stochastic discrete‐time systems: An H∞‐based approach

This paper is devoted to designing iterative learning control (ILC) for multiple‐input multiple‐output discrete‐time systems that are subject to random disturbances varying from iteration to iteration. Using the super‐vector approach to ILC, statistical expressions are presented for both expectation and variance of the tracking error, and time‐domain conditions are developed to ensure their asymptotic stability and monotonic convergence. It shows that time‐domain conditions can be tied together with an H_∞‐based condition in the frequency domain by considering the properties of block Toeplitz matrices. This makes it possible to apply the linear matrix inequality technique to describe the convergence conditions and to obtain formulas for the control law design. Furthermore, the H_∞‐based approach is shown applicable to ILC design regardless of the system relative degree, which can also be used to address issues of model uncertainty. For a class of systems with a relative degree of one, simulation tests are provided to illustrate the effectiveness of the H_∞‐based approach to robust ILC design. Copyright © 2011 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.     

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.     

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.     

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.     

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.