H ∞ Filtering of Two-Dimensional T-S Fuzzy Systems

The H _∞ filtering problem for two-dimensional Takagi–Sugeno fuzzy systems described by the Fornasini–Marchesini (FM) model is studied. Attention is focused on the design of an H _∞ fuzzy filter such that the filter error system is asymptotically stable and preserves a guaranteed H _∞ performance. By using basis-dependent Lyapunov functions and adding slack matrix variables, the coupling between the Lyapunov matrix and the system matrices is eliminated. Then, a linear matrix inequality (LMI)-based approach is developed for designing the H _∞ fuzzy filter. Finally, an illustrative example is provided to show the effectiveness of the proposed approach and less conservatism.     

Delay-Dependent Robust H ∞ Filtering for Uncertain Neutral Stochastic Time-Delay Systems

This paper is concerned with the problem of robust H _∞ filtering for neutral stochastic time-delay systems with norm-bounded parameter uncertainties. By introducing appropriate slack matrix variables, both a delay-dependent stochastic stability condition and a delay-dependent bounded real lemma are obtained in terms of linear matrix inequalities. A delay-dependent condition for the solvability of the robust H _∞ filtering problem is also proposed. Desired H _∞ filters are designed that guarantee the filtering error system to be robustly stochastically stable and satisfy a prescribed H _∞ performance level for all admissible uncertainties. A numerical example is provided to demonstrate the effectiveness of the proposed approach. This work is supported by the National Science Foundation for Distinguished Young Scholars of People’s Republic of China under Grant 60625303, the Specialized Research Fund for the Doctoral Program of Higher Education under Grant 20060288021, and the Natural Science Foundation of Jiangsu Province under Grant BK2008047.     

H ∞ Filtering Design for Linear Systems with Interval Time-Varying Delays

This paper proposes improved delay-range-dependent H _∞ performance conditions and a H _∞ filtering algorithm for linear systems with interval time-varying delays. The proposed filtering approach guarantees that the results are less conservative than those obtained by other existing approaches. Numerical examples well demonstrate the effectiveness of the proposed algorithms.     

Robust H ∞ Filtering for 2-D Systems with Intermittent Measurements

This paper is concerned with the problem of robust H _∞ filtering for uncertain two-dimensional (2-D) systems with intermittent measurements. The parameter uncertainty is assumed to be of polytopic type, and the measurements transmission is assumed to be imperfect, which is modeled by a stochastic variable satisfying the Bernoulli random binary distribution. Our attention is focused on the design of an H _∞ filter such that the filtering error system is stochastically stable and preserves a guaranteed H _∞ performance. This problem is solved in the parameter-dependent framework, which is much less conservative than the quadratic approach. By introducing some slack matrix variables, the coupling between the positive definite matrices and the system matrices is eliminated, which greatly facilitates the filter design procedure. The corresponding results are established in terms of linear matrix inequalities, which can be easily tested by using standard numerical software. An example is provided to show the effectiveness of the proposed approach. This work was partially supported by the National Natural Science Fundation of China under Grant 60504008 and 60825303, by the Research Fund for the Doctoral Program of Higher Education of China under Grant 20070213084, and by the Fok Ying Tung Education Foundation (111064).     

H ∞ Filtering for Systems with Delays and Time-varying Nonlinear Parameters

This paper is concerned with the gain-scheduled H _∞ filtering problem for a class of parameter-varying continuous systems with time delays. The systems under consideration are represented by nonlinear fractional transformation (NFT) which is a generalization of linear fractional transformation (LFT). Attention is focused on the design of a stable filter guaranteeing a prescribed disturbance attenuation level in an H _∞ sense. Sufficient solvability conditions of this problem are obtained based on Lyapunov function approach. A gain-scheduled filter can be constructed in terms of a set of linear matrix inequalities (LMIs). A numerical example is provided to demonstrate the applicability of the proposed approach.     

Reliable H ∞ Filtering for Discrete-Time Switched Singular Systems with Time-Varying Delay

This paper is concerned with the reliable H _∞ filtering problem against sensor failures for a class of discrete-time switched singular systems with time-varying delay. A practical sensor failure model, which consists of a scaling factor with upper and lower bounds to the output measuring is considered. The purpose is to design a switched full-order H _∞ filter such that, for all possible sensor failures, the resulting filtering error system is regular, causal, and uniformly asymptotically stable with a guaranteed H _∞ performance index under arbitrary switching signals. By using the switched Lyapunov function approach and establishing a finite sum equality, a delay-dependent bounded real lemma (BRL) for the filtering error systems is derived via linear matrix inequality (LMI) formulation. An improved BRL is also established by introducing additional slack matrix variables to realize the decoupling between the filtering error system matrices and the Lyapunov matrices. Then, based on the decoupled BRL, the existence criterion of the desired filter is obtained by employing the LMI technique. Some numerical examples are provided to illustrate the effectiveness and the potential of the proposed methods.     

H ∞ Fuzzy Filtering for Discrete-Time Nonlinear Systems via Fuzzy Lyapunov Function Approach

This paper is concerned with the H _∞ fuzzy filtering problem for a class of discrete-time fuzzy systems. The objective is to design a stable filter guaranteeing the asymptotic stability and a prescribed H _∞ performance of the filtering error system. Motivated by the parallel distributed compensation (PDC) technique, a new filter model is proposed in this paper. Both full-order and reduced-order filters are established, and they can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired H _∞ fuzzy filter is given. A numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach. This work was supported by the National Natural Science Foundation of China under Grant 60504020 and the Excellent Young Scholars Research Fund of the Beijing Institute of Technology 2006y0103, respectively.     

H ∞ Filtering Design for 2-D Discrete-Time Linear Systems with Polytopic Uncertainty

This technical paper studies robust H _∞ filtering design for 2-dimensional (2-D) systems and the focus is on finding other methods to further reduce the conservativeness when the ‘polynomially dependent on the parameter’ technique 2000 fails to do so. First, the possible sources of conservativeness of the existing results are explored, and then two algorithms are proposed. Since no special structures are required in the introduced variables, the algorithms can further reduce the conservativeness. In addition, the initial conditions of the algorithms are discussed and an example is provided to demonstrate the effectiveness of the conclusions.     

A Generalized Parameter-Dependent Approach to Robust H ∞ Filtering of Stochastic Systems

This paper is concerned with the problem of robust H _∞ filtering for discrete-time stochastic systems with state-dependent stochastic noises and deterministic polytopic parameter uncertainties. We utilize the polynomial parameter-dependent approach to solve the robust H _∞ filtering problem, and the proposed approach includes results in the quadratic framework that entail fixed matrices for the entire uncertain domain and results in the linearly parameter-dependent framework that use linear convex combinations of matrices as special cases. New linear matrix inequality (LMI) conditions obtained for the existence of admissible filters are developed based on homogeneous polynomial parameter-dependent matrices of arbitrary degree. As the degree grows, a test of increasing precision is obtained, providing less conservative filter designs. A numerical example is provided to illustrate the effectiveness and advantages of the filter design methods proposed in this paper. This work was supported by HKU CRCG 200611159157, the National Nature Science Foundation of China (60504008), The Research Fund for the Doctoral Programme of Higher Education of China (20070213084), the Fok Ying Tung Education Foundation (111064), and the Key Laboratory of Integrated Automation for the Process Industry (Northeastern University), Ministry of Education of China.     

Further Results on H ∞ Filtering for a Class of Discrete-Time Singular Systems with Interval Time-Varying Delay

In this paper, the problem of delay-dependent robust H _∞ filtering for discrete-time singular systems with time-varying delay and polytopic uncertainties is investigated. Without introducing the free-weighting matrices to deal with the cross terms, a delay-dependent H _∞ performance analysis result is established for error singular system by considering the relationship between the time-varying delay and its bounds at first. Based on this result, a linear robust H _∞ filter is designed such that the filtering error singular system is regular, causal and asymptotically stable with a H _∞ norm bound. Numerical examples are given to show the advantages of the proposed results.     

Delay-Dependent Nonfragile Robust H ∞ Filtering of T–S Fuzzy Time-Delay Systems

The problem of nonfragile robust H _∞ filtering for a class of Takagi–Sugeno fuzzy time-delay systems is investigated in the paper. We design a fuzzy filter which can tolerate some level of the filter gain variations while ensuring both the robust stability and a prescribed H _∞ performance level of the filtering error system. Delay-dependent sufficient conditions for the existence of such filters are obtained in terms of linear matrix inequalities, and an explicit expression of a desired filter is given.     

l 2–l ∞ Filtering Design for Piecewise Discrete-Time Linear Systems

This paper is concerned with the l ₂–l _∞ filtering problem for a class of piecewise discrete-time linear systems. Attention is focused on the design of a stable filter guaranteeing a prescribed noise attenuation level in the l ₂–l _∞ sense. By using the piecewise Lyapunov function, a sufficient condition for the solvability of this problem is obtained in terms of linear matrix inequalities (LMIs). It has been shown that the l ₂–l _∞ filtering problem can be solved as an LMI optimization problem. Two numerical examples are presented to demonstrate the validity of the proposed design method.     

Weighted H ∞ Filtering of Switched Systems with Time-Varying Delay: Average Dwell Time Approach

This paper is concerned with the H _∞ filtering problem for a continuous-time linear switched system with time-varying delay in its state. To reduce the overdesign of the quadratic framework, this paper proposes a parameter-dependent filter design procedure, which is much less conservative than the quadratic approach. By using an average dwell time approach and the piecewise Lyapunov function technique, a sufficient condition is first proposed to guarantee the exponential stability with a weighted H _∞ performance for the filtering error system with the decay estimate explicitly given. Then, the corresponding solvability condition for a desired filter is established, and the filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical software. All the conditions obtained in this paper are delay dependent. Finally, a numerical example is given to illustrate the effectiveness of the proposed theory.     

l 2–l ∞ Filtering for Multirate Systems Based on Lifted Models

For a multirate sample-data system where the output sampling rate is slower than the input updating rate, we study the l ₂–l _∞ filtering problems for fast state estimation by using the lifted model. The filtering problem is handled in the framework of linear matrix inequalities (LMIs) with a nonconvex constraint, which is numerically solved by the product reduction algorithm. Finally, the effectiveness of the proposed method is illustrated and verified by simulation examples. This research was supported by the Natural Sciences and Engineering Research Council of Canada and the Canada Foundation for Innovation and the National Natural Science Foundation of China (60372105 and 60672118).     

H ∞ Filtering for Markovian Switching System with Mode-Dependent Time-Varying Delays

This paper deals with the problem of H _∞ filtering for Markovian switching systems. The system under consideration involves discrete and mode-dependent time-varying delays. The aim of this paper is to design a filter such that the filtering error system is stochastically stable with a prescribed H _∞ disturbance attenuation level. Sufficient conditions for the existence of H _∞ filters are expressed in terms of linear matrix inequalities (LMIs), which can be solved by using Matlab LMI control toolbox. Numerical examples are given by including a transmission control protocol (TCP) network model to illustrate the practical importance and effectiveness of the proposed main results.     

A Generalized KYP Lemma-Based Approach for H ∞ Control of Singularly Perturbed Systems

In this paper, H _∞ control synthesis of linear time invariant singularly perturbed systems (SPS) based on a generalized KYP lemma approach is investigated. By employing a generalized KYP lemma on the low- and high-frequency domains of SPS, respectively, a slow (low-frequency) controller and a fast (high-frequency) controller are designed to stabilize the slow and fast subsystems, and also to meet the individual H _∞ performance specifications. A composite controller for the full-order SPS is constructed via the above two above well-defined lower-order problems. Moreover, the effectiveness of the proposed method is verified as compared with the traditional H _∞ design method by its application to a tracking problem of SPS and an H _∞ model matching problem for SPS.     

A Delay Partitioning Approach to H �� Filtering for?Continuous Time-Delay Systems

This paper investigates the problem of delay-dependent H _∞ filter design for continuous time-delay systems. Attention is focused on the design of linear filters guaranteeing a prescribed noise attenuation level in an H _∞ sense. The admissible filters can be obtained from the solution of a convex optimization problem in terms of linear matrix inequalities (LMIs), which can be readily solved via standard software. The crucial issue for solving the filter design problem is the utilization of the delay partitioning idea, which proves to be less conservative than most of the existing results, and the conservatism could be notably reduced by thinning the delay partitioning. Numerical examples are provided to show the effectiveness and the advantage of the proposed filter design method.     

Robust H ∞ Control for a Class of 2-D Nonlinear Discrete Stochastic Systems

This paper is concerned with the problem of stability and robust H _∞ control for 2-D stochastic systems with parameter uncertainties and sector nonlinearities. The class of systems under investigation is described by the 2-D state-space Roesser model. Our attention is focused on the design of a state feedback controller for 2-D stochastic system with sector nonlinearity, such that the closed-loop 2-D stochastic system is asymptotically stable and has a prescribed H _∞ disturbance attenuation performance. First, a sufficient condition is established for the 2-D nonlinear stochastic systems to be asymptotically stable. Then, we extend the bounded real lemma for 2-D systems to 2-D stochastic systems with sector nonlinearities. Based on this lemma, solvability conditions for the H _∞ control of 2-D nonlinear stochastic systems in the form of LMIs (linear matrix inequalities) are derived. A numerical example illustrates the effectiveness of the proposed results.     

Finite-Time H ∞ Inverse Optimal Control of Affine Nonlinear Systems

This paper is focused on the problem of the finite-time H _∞ inverse optimal control for affine nonlinear systems. Based on the finite-time control Lyapunov function, we derive a sufficient condition for the existence of time-invariant, continuous, finite-time stabilizing and inverse optimal state feedback control law, and propose a universal formula for constructing the finite-time H _∞ inverse optimal control law. We investigate the relationship between the finite-time stabilization and the finite-time H _∞ inverse optimal control. Finally, some examples are given to illustrate the effectiveness of the presented results.     

H ∞ Control of Piecewise-Linear Systems Under Unreliable Communication Links

This paper considers the problem of H _∞ control of piecewise-linear control systems under unreliable communication links. Due to the limited bandwidth of the channels, signal transmission delays and data packet losses can occur between the plant and the controller. In the presence of random signal transmission delays and data packet losses, a piecewise controller is designed to stabilize the piecewise-linear system in the sense of mean square and also achieve a prescribed H _∞ disturbance attenuation performance based on piecewise-quadratic Lyapunov–Krasovskii functionals. It is shown that the H _∞ controllers can be designed by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. Moreover, the controller design method is further extended to uncertain case where the system matrices’ uncertainties are represented in polytopic frameworks. Finally, an example is provided to illustrate the effectiveness of the developed theoretical results.