Robust Stochastic Stabilization and H �� Control for?Neutral Stochastic Systems with Distributed Delays

This paper considers the problem of robust stabilization and H _∞ control for a class of uncertain neutral stochastic systems, in which delay is distributed and the parametric uncertainties are norm-bounded. By designing a state feedback controller, we obtain a delay-dependent criterion such that the resulting closed-loop system is robustly stochastically asymptotically stable in the mean square and the effect of the disturbance input on the controlled output is less than a prescribed level for all admissible parameter uncertainties. New sufficient conditions are presented based on the linear matrix inequality approach. Finally, numerical examples are used to illustrate the effectiveness and feasibility of the approaches proposed in this paper.     

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 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.     

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.     

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.     

Robust Non-Fragile Guaranteed Cost Control for Nonlinear Time Delay Discrete-Time Systems Based on T-S Model

This paper concerns the robust non-fragile guaranteed cost control for nonlinear time delay discrete-time systems based on Takagi-Sugeno （T-S） model. The problem is to design a guaranteed cost state feedback controller which can tolerate uncertainties from both models and gain variation. Sufficient conditions for the existence of such controller are given based on the linear matrix inequality （LMI） approach combined with Lyapunov method and inequality technique. A numerical example is given to illustrate the feasibility and effectiveness of our result.     

New Stability Criteria for Neural Networks with Distributed and Probabilistic Delays

This paper is concerned with the stability analysis of neural networks with distributed and probabilistic delays. The probabilistic delay satisfies a certain probability distribution. By introducing a stochastic variable with a Bernoulli distribution, the neural network with random time delays is transformed into one with deterministic delays and stochastic parameters. New conditions for the exponential stability of such neural networks are obtained by employing new Lyapunov–Krasovskii functionals and novel techniques for achieving delay dependence. The proposed conditions reduce the conservatism by considering not only the range of the time delays, but also the probability distribution of their variation. A numerical example is provided to show the advantages of the proposed techniques. This work was partially supported by National Natural Science Foundation of China (60528007 and 60825303), the Research Fund for the Doctoral Programme of Higher Education of China (20070213084), RGC HKU 7028/04P, Hong Kong, China, and EPSRC (EP/F029195), UK.     

Robust H ∞ Output Tracking Control for a Class of Nonlinear Systems with Time-Varying Delays

This paper addresses the H _∞ output tracking problem for a class of nonlinear systems subjected to model uncertainties and with interval time-varying delay. The stability of the nonlinear time-delay system is analyzed with a novel delay-interval-dependent Lyapunov–Krasovskii functional. Compared to state-of-the-art criteria for linear and nonlinear time-delay systems, less conservative stability conditions are derived with the introduction of new delay-interval-dependent terms and the exploitation of the delay subintervals size. The proposed analysis considers that the delay derivative is either upper and lower bounded, bounded above only, or unbounded, i.e., no restrictions are cast upon the derivative. Numerical examples are provided to enlighten the importance and advantages of the present criterion which outperforms previous criteria in time-delay systems literature. Also, an additional example is provided to highlight the effectiveness of the proposed H _∞ output tracking control design technique for complex nonlinear systems with time-varying delay.     

Event-Based Reliable H∞ Control for Networked Control System with Probabilistic Actuator Faults

This paper investigates the reliable con- troller design for networked control system with proba- bilistic actuator faults under event-triggered scheme. The key idea is that only the newly states violating specified triggering condition will be transmitted to the controller. Considering the effect of the network transmission delay, event-triggered scheme and probabUistic actuator faults with different failure rates, a new actuator fault model is proposed. Criteria for the exponential stability and criteria for co-designing both the feedback and the trigger param- eters are derived by using Lyapunov functional. These cri- teria are obtained in the form of linear matrix inequalities. A simulation example is employed to show the effectiveness of the proposed 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.     

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).     

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.     

An Approach to H ∞ Control of a Class of Nonlinear Stochastic Systems

This paper studies the problems of the stochastic stabilization and H _∞ control of a class of nonlinear stochastic systems that can be represented by a stochastic heterogeneous model. Based on this model, the problem of stabilization with state feedback controller is first considered, and a new H _∞ controller design method is then developed. Synthesis of both stabilization and H _∞ controller is based on the solutions of linear matrix inequalities (LMIs). Finally, an example is given to illustrate the effectiveness of the approach proposed in this paper.     

Robust H ∞ Control for Class of Discrete-Time Markovian Jump Systems with Time-Varying Delays Based on Delta Operator

In this paper, the problem of robust H _∞ state feedback control using a delta operator approach for a class of linear fractional uncertain jump systems with time-varying delays is investigated. Based on the Lyapunov–Krasovskii functional in the delta domain, a new delay-dependent H _∞ state feedback controller which requires both robust stability and a prescribed H _∞ performance is presented in terms of linear matrix inequalities. The sampling period T appears as an explicit parameter; therefore, it is easy to observe and analyze the effect of the results with different sampling periods. Furthermore, the proposed method can unify some previous related continuous and discrete systems into the framework of delta operator systems. Numerical examples are presented to illustrate the effectiveness of the developed techniques.     

Observer-Based H ∞ Synchronization and Unknown Input Recovery for a Class of Digital Nonlinear Systems

This paper considers the synchronization and unknown input recovery problem for a class of digital nonlinear systems based on a nonlinear observer approach. A generalized Luenberger-like observer is introduced for a class of discrete-time Lipschitz nonlinear systems. Stability conditions for the existence of asymptotic observers are established in terms of some linear matrix inequalities. It is shown that the proposed conditions are less conservative than some existing ones in the recent literature. Moreover, an observer design method is used to address the problem of H _∞ synchronization and unknown input recovery for a class of Lipschitz nonlinear systems in the presence of disturbances in both the state and output equations. Finally, a numerical example is provided to illustrate the effectiveness of the proposed design.     

Modeling and Stability Analysis for Non-linear Network Control System Based on T-S Fuzzy Model

Based on the T -S fuzzy model, this paper presents a new model of non -linear network control system with stochastic transfer delay. Sufficient criterion is proposed to guarantee globally asymptotically stability of this two - levels T - S fuzzy model. Also a T - S fuzzy observer of NCS is designed base on this two - levels T - S fuzzy model. All these results present a new approach for networked control system analysis and design.     

Fault Detection for Networked Nonlinear Systems with Time Delays and Packet Dropouts

This paper addresses the problem of fault detection (FD) for networked systems with global Lipschitz nonlinearities and incomplete measurements, including time delays and packet dropouts which are described by a more general model using Markov jump system approach. We aim to design a mode-dependent fault detection filter (FDF) such that, for all external disturbances and incomplete measurements, the error between the residual and fault is made as small as possible. The addressed FD problem is then converted into an auxiliary H _∞ filtering problem of Markov jump system with time-varying delay. By applying Lyapunov–Krasovskii approach, a sufficient condition for the existence of the FDF is derived in terms of certain linear matrix inequalities (LMIs). When these LMIs are feasible, the explicit expression of the desired FDF can also be characterized. A numerical example is exploited to show the effectiveness of the results obtained.     

Stabilization of Discrete-Time Switched Systems with Input Time Delay and Its Applications in Networked Control Systems

In this paper, we focus on investigating the asymptotic stabilizability of switched systems with input time delay and its applications in networked control systems (NCSs). First, based on an important lemma, a linear matrix inequality (LMI)-based asymptotic stabilizability criterion is established. Stabilizing switched state feedback controllers can be designed by solving a set of LMIs, which can be easily tested with efficient LMI algorithms. Then, for NCSs with communication constraints, the NCS is modelled as a discrete-time switched system with input time delay. Thus, the asymptotic stabilizability criterion of switched system with input delay can be applicable to such NCSs. Finally, an example is given to illustrate our main results. This work is supported by the National Natural Science Foundation of China under grants (No. 60704015), a grant of Liuhui Center for Applied Mathematics of Nankai University and Tianjin University in China.     

Relaxed H ∞ Controller Design for Continuous Markov Jump System with Incomplete Transition Probabilities

This paper studies the H _∞ state feedback control of continuous-time Markov jump linear systems (MJLSs) with incomplete transition probabilities (TPs) which are allowed to be known, uncertain with known lower and upper bounds, and completely unknown. Combining the TP property and a matrix transformation technique, a new method for the H _∞ controller synthesis is proposed in terms of linear matrix inequalities (LMIs). The dominant feature of the proposed method is that two sets of slack variables without coupling relationship are introduced. It is shown that the proposed method is less conservative than the existing result. The effectiveness of the proposed method is further illustrated by numerical examples.