A new approach to H∞ filtering for linear time-delay systems

This paper proposes a class of $H_{\infty }$ filter design for continue-time systems with time-varying delay. Firstly, by exploiting a new Lyapunov function and using the convexity property of the matrix inequality, some delay-dependent stability conditions can be obtained for the asymptotical stability of the filtering-error system, which can lead to much less conservative analysis results. Secondly, based on the obtained conditions, the filter parameter matrixes can be obtained in terms of linear matrix inequalities (LMIs). Finally, two examples are given to demonstrate the effectiveness and the merit of the proposed method.     

Novel master–slave synchronization criteria of chaotic Lur’e systems with time delays using sampled-data control

This paper investigates the problem of master–slave synchronization of chaotic Lur’e systems (CLSs) with time delays by sampled-data control. First, a novel Lyapunov–Krasovskii functional (LKF) is constructed with some new augmented terms, which can fully capture the system characteristics and the available information on the actual sampling pattern. In comparison with existing results, the constraint condition of the positive definition of the LKF is more relax, since it is positive definite only requiring at sampling instants. Second, based on the LKF, a less conservative synchronization criterion is established. Third, the desired estimator gain can be designed in terms of the solution to linear matrix inequalities (LMIs). The obtained conditions ensure the master–slave synchronization of CLSs under a longer sampling period than remarkable existing works. Finally, three numerical simulations of Chua’s circuit and neural network are provided to show the effectiveness and advantages of the proposed results.     

Absolute stability and Lyapunov–Krasovskii functionals for switched nonlinear systems with time-delay

We derive conditions for the existence of Lyapunov–Krasovskii functionals for a number of classes of nonlinear switched systems with time-delay. In particular, we first give conditions for systems of retarded type that relax those recently described in Sun and Wang (2013) [18]. Using similar techniques, related results are then derived for coupled differential-difference systems and for systems of neutral type. Finally, we briefly note some corresponding results for discrete-time systems.     

New robust H∞ control for uncertain stochastic Markovian jumping systems with mixed delays based on decoupling method

This paper considers the problems of robust stochastic stabilization and robust $H_{\infty }$ controller design for a class of stochastic Markovain jumping systems with mixed time delays and polytopic parameter uncertainties. Both the interval time-varying delay and distributed time delay are simultaneously considered. Some new delay-dependent sufficient conditions, which differs greatly from the most existing results, are obtained based on the decoupling method and some advanced techniques. A numerical example is provided to illustrate the effectiveness of the proposed criteria.     

A state estimation H∞ issue for discrete-time stochastic impulsive genetic regulatory networks in the presence of leakage,multiple delays and Markovian jumping parameters

In this work, we probes the stability results of H_∞ state estimation for discrete-time stochastic genetic regulatory networks with leakage, distributed delays, Markovian jumping parameters and impulsive effects. Here, we focus to evaluate the true absorption of mRNAs and proteins by calculating the H_∞ estimator in such a way that the estimation error dynamics is stochastically stable during the completion of the prescribed H_∞ disturbance attenuation level. In favor of decreasing the data communion in trouble, the H_∞ system accept and evaluate the outputs that are only transferred to the estimator when a certain case is acroses. Further, few sufficient conditions are formulated, by utilizing the Lyapunov–Krasovskii functional under which the estimation error system is stochastically stable and also satisfied the H_∞ attainment constraint. The estimator is obtained in terms of linear matrix inequalities (LMIs) and these LMIs are attainable, only if the estimator gains can be absolutely given. In addition to that, two numerical examples are exposed to establish the efficiency of our obtained results.     

Robust H∞ control for a class of uncertain nonlinear systems with mixed time-delays

This paper is concerned with the robust H_∞ control problem for a general class of uncertain nonlinear systems with mixed time-delays. The mixed time-delays consist of both discrete and distributed delays. We aim to design a memoryless state feedback controller such that the closed-loop system is robustly stable for all admissible uncertainties with guaranteed H_∞ disturbance rejection attenuation level. By introducing a new Lyapunov–Krasovskii functional that reflects the mixed delays, sufficient conditions are established for the closed-loop system ensuring the robust stability as well as the H_∞ performance requirement. The controller design is facilitated in terms of the solvability of a Hamilton–Jacobi inequality. Two numerical examples are utilized to demonstrate the effectiveness of the proposed methods.     

State estimation of neutral Markovian jump systems: A relaxed L–K functional approach

This paper investigates the state estimation problem of uncertain neutral delay systems with Markovian jumping parameters. First, a novel Lyapunov–Krasovskii (L–K) functional containing the interconnected information between neutral and discrete delay is proposed. Then, based on Jensen’s integral and Wirtinger-based inequality, the obtained results are improved by relaxing the positive-definiteness restrictions on Lyapunov matrices. Third, the state estimators are designed to guarantee the asymptotic stability of the error state system. Finally, numerical examples are provided to show the effectiveness of the proposed results.     

Non-fragile quantized H∞ output feedback control for nonlinear systems with quantized inputs and outputs

This paper is concerned with non-fragile $H_{\infty }$ control problems for a class of continuous-time nonlinear systems with unknown nonlinearity and quantized inputs and outputs. The construction of both static output feedback (SOF) and observer-based output feedback (OBOF) control laws in the presence of additive interval-bounded controller coefficient variations can be divided into two parts, linear and nonlinear parts. The linear part plays a role in achieving the $H_{\infty }$ performance, while the nonlinear part is used to reduce the quantization effect. However, it should be pointed out that the effect of input and output quantization can be eliminated fully for SOF case by requiring knowledge of all signs of the states, but only the effect of input quantization can be eliminated for OBOF case. It is worth mentioning that three novel alternative methods with strict linear matrix inequality (LMI) conditions are proposed to design both SOF and OBOF controllers. In particular, these three new methods do not introduce any other auxiliary constraints as many existing results do where a matrix equality constraint between system matrix and Lyapunov matrix is often inserted. Finally, the effectiveness and advantages of the proposed control methods are demonstrated by a numerical example.     

H∞ tracking control for a class of asynchronous switched nonlinear systems with uncertain input delay

This paper studies the problems of stability and H∞ model reference tracking performance for a class of asynchronous switched nonlinear systems with uncertain input delay. First, it is assumed switched controller and corresponding piecewise Lyapunov function are unknown but the derivative of piecewise Lyapunov function has a condition; this condition implies that the nominal system (system without input delay and disturbance) is exponentially stable by any switched controller which satisfies this condition. With this assumption, a proper Lyapunov–Krasovskii functional is constructed. By employing this new functional and average dwell time technique, the delay-dependent input-to-state stability criteria are derived under a certain delay bound; in addition, a mechanism which finds the upper bound of input delay is proposed. Finally, a kind of state feedback control law which fulfils condition of aforesaid piecewise Lyapunov function is introduced to guarantee the input-to-state stability and H∞ model reference tracking performance. Simulation examples are presented to demonstrate the efficacy of results.     

An event-triggered approach to distributed H∞ state estimation for state-saturated systems with randomly occurring mixed delays

In this paper, the event-triggered distributed H_∞ state estimation problem is investigated for a class of state-saturated systems with randomly occurring mixed delays over sensor networks. The mixed delays, which comprise both discrete and distributed delays, are allowed to occur in a random manner governed by two mutually independent Bernoulli distributed random variables. In order to alleviate the communication burden, an event-triggered mechanism is utilized for each sensor node to decide whether or not its current information should be broadcasted to its neighbors. The aim of this paper is to design event-triggered state estimators such that the error dynamics of state estimation is exponentially mean-square stable with a prescribed H_∞ performance index. By resorting to intensive stochastic analysis, sufficient conditions are first derived to guarantee the existence of the desired estimators, and the parameters of the desired distributed estimators are then obtained in light of the feasibility of a certain set of matrix inequalities. A numerical example is employed to illustrate the usefulness of the proposed distributed estimation algorithm.     

Quadratically convex combination approach to stability of T–S fuzzy systems with time-varying delay

This paper develops a novel stability analysis method for Takagi–Sugeno (T–S) fuzzy systems with time-varying delay. New delay-dependent stability criteria in terms of linear matrix inequalities for time-varying delayed T–S fuzzy systems are derived by the newly proposed augmented Lyapunov–Krasovski (L–K) functional. This functional contains the cross terms of variables and quadratic terms multiplied by a higher degree scalar function. Different from previous results, our derivation applies the idea of second-order convex combination, and the property of quadratic convex function without resorting to the Jensen's inequality. Two numerical examples are provided to verify the effectiveness of the presented results.     

Robust synchronization of uncertain Markovian jump complex dynamical networks with time-varying delays and reaction–diffusion terms via sampled-data control

This paper is concerned with the problem of robust synchronization of a class of complex dynamical networks with time-varying delays and reaction–diffusion terms. To reflect most of the dynamical behaviors of the system, the parameter uncertainties are considered. A sampled-data controller with m stochastically varying sampling periods whose occurrence probabilities are given constants is considered. The control objective is that the trajectories of the system by designing suitable control schemes track the trajectories of the system with sample-data control. It is shown that, through Lyapunov stability theory, the proposed sample-data controllers are successful in ensuring the achievement of robust synchronization of complex dynamical networks even in the case of uncertainity and Markovian jumping parameters. By utilizing the Lyapunov functional method, Jensen’s inequality, Wirtinger’s inequality and lower bounds theorem, we establish a sufficient criterion such that, for all admissible parameter uncertainties, the complex dynamical network is robustly synchronized. The derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.     

Exponential stabilization and sampled-date H∞ control for uncertain T–S fuzzy systems with time-varying delay

In this paper, the exponential stabilization problem of uncertain T–S fuzzy systems with time-varying delay is emulated by fuzzy sampled-data H_∞ control. Firstly, a novel suitable Lyapunov–Krasovskii function is constructed, which contains all the information about the sampling pattern. Secondly, a less conservative result is achieved by using an extended Jensen inequality, and purposefully using a compact free weighting matrix. In addition, according to the linear matrix inequality (LMI), some sampled-data H_∞ exponential stability sufficient conditions and controller design of T–S fuzzy systems are established. Finally, effectiveness gives some illustrative examples may be used to display the value of the current proposed method as well as a significant improvement.     

Mixed H∞ and passive control for a class of nonlinear switched systems with average dwell time via hybrid control approach

This paper investigates the mixed H_∞ and passive control problem for a class of nonlinear switched systems based on a hybrid control strategy. To solve this problem, firstly, using the Takagi–Sugeno (T–S) fuzzy model to approximate every nonlinear subsystem, the nonlinear switched systems are modeled as the switched T–S fuzzy systems. Secondly, the hybrid controllers are used to stabilize the switched T–S fuzzy systems. The hybrid controllers consist of dynamic output-feedback controllers for every subsystem and state updating controllers at the switching instant. Thirdly, a new performance index is proposed for switched systems. This new performance index can be viewed as the mixed weighted H_∞ and passivity performance. Based on this new performance index, the weighted H_∞ control problem and the passive control problem for switched T–S fuzzy systems via the hybrid control strategy are solved in a unified framework. Together the multiple Lyapunov functions (MLFs) approach with the average dwell time (ADT) technique, new design conditions for the hybrid controllers are obtained. Under these conditions, the closed-loop switched T–S fuzzy systems are globally uniformly asymptotically stable with a prescribed mixed H_∞ and passivity performance index. Moreover, the desired hybrid controllers can be constructed by solving a set of linear matrix inequalities (LMIs). Finally, the effectiveness of the obtained results is illustrated by a numerical example.