Further Results on Robust Variance-Constrained Filtering for Uncertain Stochastic Systems with Missing Measurements

This paper revisits the problem of robust filtering for uncertain discrete-time stochastic systems with missing measurements. The measurements of the system may be unavailable at any sample time. Our aim is to design a new filter such that the error state of the filtering process is mean-square bounded. Furthermore, the steady-state variance of the estimation error of each state does not exceed the individual prescribed upper bound subject to all admissible uncertainties and all possible incomplete observations. It is shown that the design of a robust filter can be carried out by directly solving a set of linear matrix inequalities. The nonsingular assumption on the system matrix A and the inequality which is used to handle the uncertainties are not necessary in the derivation process of our results. Thus, it is expected that a less conservative condition can be obtained. The advantage of the new method is demonstrated via an illustrative example.     

Robust Absolute Stability Criterion for Uncertain Lur’e Differential Inclusion Systems with Time Delay

This paper deals with uncertain Lur’e differential inclusion systems with time delay. The set-valued mappings considered are upper semi-continuous, non-empty, closed, convex and bounded. It is proved that original systems can be reduced to their equivalent systems by introducing the dynamic multiplier. Based on the Lyapunov–Krasovskii functional, delay-dependent stability criterion is given to guarantee the robust absolute stability of the systems by LMI method. The result is new to the previous literature. Numerical examples are provided to show the effectiveness of the proposed stability condition.     

Delay-Dependent Robust H ∞ Filter Design for Uncertain Linear Systems with Time-Varying Delay

A new delay-dependent robust H _∞ filtering design for uncertain linear systems with time-varying delay is investigated. Two kinds of time-varying delays are considered. One is differentiable uniformly bounded with a bounded delay derivative; the other is continuous uniformly bounded. A full-order filter is designed which ensures the asymptotic stability of the filtering error system and a prescribed level of H _∞ performance for all possible parameters which reside in a given polytope. By constructing a new Lyapunov functional which contains a triple integral term, new delay-dependent conditions for the existence of the H _∞ filter are derived which are less conservative than the existing ones. The filter gain can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, two numerical examples are given to show the effectiveness and the advantages of the proposed method.     

Robust Exponential Stability Criteria for T–S Fuzzy Stochastic Delayed Neural Networks of Neutral Type

This paper is concerned with the problem of robust exponential stability for T–S fuzzy stochastic neural networks of neutral type. Based on the Lyapunov–Krasovskii functional and stochastic analysis approach, new delay-dependent stability criteria are established in terms of linear matrix inequalities (LMIs) which can be checked easily by the LMI Control Toolbox in MATLAB. Finally, numerical examples are given to illustrate the feasibility and effectiveness of the proposed method.     

Stability of Nonlinear Networked Control System with Uncertainties

The problems of signal transmission delay, actuator data packet dropout, and measurement quantization in nonlinear networked control systems are investigated in this paper. First, a nonlinear system is represented as a series of linear systems through T–S fuzzy modeling, then the problem of actuator data packet dropout is solved through the introduction of a diagonal matrix; second, the problem of maintaining order is solved through the ZOH, and the problem of limited bandwidth is solved through the measurement quantization; and finally, the controller is designed to compensate the actuator data packet dropout.     

A New Robust Stabilization Analysis Result for Uncertain Systems with Time-Varying Delay

Time delay and uncertainty are frequently encountered in various engineering systems. The robust stabilization problem for uncertain systems with time-delay has been paid more attentions by many researchers[1-8]. Most results of the robust stabilization are based on the systems matrices norm approach. The uncertainties of the systems discussed there must satisfy the so-called matching-conditions, which is more strict for the practical systems. The memoryless state feedback control gain matrice…     

Delay-Dependent Robust H ∞ Admissibility and Stabilization for Uncertain Singular System with Markovian Jumping Parameters

This paper investigates the problem of delay-dependent robust H _∞ admissibility and stabilization for uncertain singular time delay systems with Markovian jumping parameters. The considered systems are not necessarily assumed to be regular and impulse-free. In terms of the linear matrix inequality (LMI) approach, a delay-dependent stochastic admissibility criterion is given to ensure that the nominal system is regular, impulse-free and stochastically stable. Based on this criterion, the problem is solved. A numerical example is provided to demonstrate the efficiency of the proposed methods in this paper. This work is supported by the National “863” Key Program of China (2008AA042902), the National Natural Science Foundation of China (60874113), the Doctor Base Foundation of Colleges and Universities by the Ministry of Education of China (200802550007) and the Key Scientific Research and Innovation Program of Shanghai Education Committee (09zz66).     

Delay-dependent H ∞ Control for Uncertain 2-D Discrete Systems with State Delay in the Roesser Model

This paper is concerned with the problem of H _∞ control for uncertain two-dimensional (2-D) state delay systems described by the Roesser model. Based on a summation inequality, a sufficient condition to have a delay-dependent H _∞ noise attenuation for this 2-D system is given in terms of linear matrix inequalities (LMIs). A delay-dependent optimal state feedback H _∞ controller is obtained by solving an LMI optimization problem. Finally, a simulation example of thermal processes is given to illustrate the effectiveness of the proposed results.     

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.     

Robust H ∞ Control for a Class of Uncertain Neutral Stochastic Systems with Mixed Delays: a CCL Approach

In this paper, the problem of robust H _∞ control for a class of uncertain neutral stochastic systems with mixed delays is investigated. The parameter uncertainties are assumed to be norm-bounded. A delay-dependent sufficient condition is derived in terms of the nonlinear matrix inequality by constructing proper Lyapunov–Krasovskii functional, using matrix inequality techniques and introducing free weighting matrices. The new result obtained in this paper can be tested numerically by using the so-called cone complementarity linearization (CCL) algorithm. Two examples provided in the literature show the effectiveness of the proposed approach.     

Robust H �� Filtering for Uncertain Nonlinear Stochastic Systems with Mode-dependent Time-delays and Markovian Jump Parameters

This paper investigates the problem of robust H _∞ filtering for a class of uncertain nonlinear stochastic time-delay systems with Markovian jump parameters. The system under consideration contains parameter uncertainties, It?-type stochastic disturbances, unknown nonlinearities as well as time-varying delays, which vary in a range and dependent on the mode of the operation. We aim to design a full-order Markovian jump filter such that, for all admissible uncertainties, the filtering error system is robustly asymptotically stable in the mean square, and a prescribed H _∞ disturbance attenuation level is guaranteed. By using the Lyapunov stability theory and It? differential rule, some sufficient conditions in terms of linear matrix inequality (LMI) are proposed to guarantee the existence of the desired H _∞ filter. Then, the explicit expressions of the desired filter parameters are given. Illustrative examples are provided to demonstrate the effectiveness and applicability of the proposed method.     

Robust Stability Analysis of Takagi–Sugeno Fuzzy Nonlinear Singular Systems with Time-Varying Delays Using Delay Decomposition Approach

This paper investigates the problem of robust stability analysis for Takagi–Sugeno fuzzy nonlinear singular systems with time-varying delays. The nonlinear functions are assumed to satisfy the Lipschitz conditions. By constructing Lyapunov–Krasovskii functional with different weighted matrices, sufficient delay-dependent asymptotic stability conditions are expressed in terms of linear matrix inequalities. Further, delay decomposition approach is used to derive less conservative results. The effectiveness of the derived theoretical result is shown through numerical examples.     

Stability for Cellular Neural Networks with Delay

The cellular neural networks with delay (DCNN‘s) are investigated, and some new sufficient conditions on asymptotical stability of DCNN‘s are derived by constructing the Liapunov functional and utilizing M-matrix and the ω-limit set. It is shown that the new conditions are not related to the delayed parameter.     

A Delay-Dependent Approach to Robust H ∞ Control for Uncertain Stochastic Systems with State and Input Delays

In this paper, the problem of delay-dependent robust H _∞ control for uncertain stochastic systems with state and input delays is investigated. The time delays are assumed to be bounded and time varying and the uncertainties are assumed to be norm bounded. By using the Lyapunov functional method, a new delay-dependent robust H _∞ control scheme is presented in terms of linear matrix inequalities (LMIs). Some numerical examples are given to illustrate the effectiveness of the proposed approach. This work is partially supported by the Natural Science Foundation of China (60674055, 60774047), and the Taishan Scholar Programme of Shandong Province. An erratum to this article can be found at     

Robust Stabilization Analysis for Uncertain Systems with Time-Varying Delays

Many techniques have been proposed to stabilize uncertain systems with state delay via state feedback in Ref.[1~12], LI et al. investigated the approach of linear matrix inequality (LMI) [1,5], Mori, Su et al. discussed the robust stabilization where the uncertainty satisfies the so-called matching conditions, by using the property of LMI[2,3]. Perterson et al. introduced a Ricatti equation approach[6], Hoi, Shen et al., designed the state feedback controller to stabilize the uncertain dy…     

Exponential H ∞ Output Tracking Control for Switched Neutral System with Time-Varying Delay and Nonlinear Perturbations

In this paper, the problem of exponential H _∞ output tracking control is addressed for a class of switched neutral system with time-varying delay and nonlinear perturbations. The considered system consists of different neutral and discrete delays. By resorting to the average dwell time approach, a new Lyapunov–Krasovskii functional is proposed to establish sufficient conditions for the exponential stability and H _∞ performance of switched neutral systems. Then, the problem of exponential H _∞ output tracking control is investigated, an explicit expression for the desired exponential tracking controller is also given. Finally, a numerical example is provided to demonstrate the potential effectiveness of the proposed method.     

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.     

LMI Conditions for Robust Stability Analysis of?Stochastic Hopfield Neural Networks with Interval Time-Varying Delays and Linear Fractional Uncertainties

In this paper, the delay-dependent robust stability for a class of stochastic neural networks with linear fractional uncertainties is studied. The time-varying delay is assumed to belong to an interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the Lyapunov–Krasovskii functional, stochastic stability theory and some inequality techniques, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs). In order to derive less conservative results, few free-weighting matrices are introduced. Three numerical examples are presented to show the effectiveness and improvement of the proposed method.     

Global Exponential Stability of Almost Periodic Solution of Cellular Neural Networks with Time-Varying Delays

In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays （CNNVDs） is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.