Event-based H∞ filtering for discrete-time Markov jump systems with network-induced delay

The problem of event-based H_∞ filtering for discrete-time Markov jump system with network-induced delay is investigated in this paper. For different jumping modes, different event-triggered communication schemes are constructed to choose which output signals should be transmitted. Through the analysis of network-induced delay’s intervals, the discrete-time system, the event-triggered scheme and network-induced delay are unified into a discrete-time Markov jump filter error system with time-delay. Based on time-delay system analysis method, criteria are derived to guarantee the discrete-time Markov jump error system stochastically stable with an H_∞ norm bound. The correspondent filter and the event-based parameters are also given. A numerical example is given to show that the proposed filter design techniques are effective and event-triggered communication scheme can save limited network resources greatly.     

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.     

Asynchronous H∞ fixed-order filtering for LPV switched delay systems with mode-dependent average dwell time

This paper investigates the problem of robust H_∞ fixed-order filtering for a class of linear parameter-varying (LPV) switched delay systems under asynchronous switching that the system parameter matrices and the time delays are dependent on the real-time measured parameters. The so-called asynchronous switching means that there are time delays between the switching of filters and the switching of system modes. By constructing the parameter-dependent and mode-dependent Lyapunov-Krasovskii functional which is allowed to increase during the running time of active subsystem with the mismatched filter, and using the mode-dependent average dwell time (MDADT) switching method, the sufficient conditions for exponential stability and satisfying a novel weighted H_∞ criterion are derived. As there exist couplings between Lyapunov-Krasovskii functional matrices and system parameter matrices, we utilize slack matrices to decouple them. Based on the above results, a suitable weighted H_∞ fixed-order filter can be obtained in the form of the parameter linear matrix inequalities (PLMIs). By virtue of approximate basis function and gridding technique, the design of weighted H_∞ fixed-order filter can be transformed into the solution of the finite dimensional LMIs. Finally, a numerical example is presented to verify both the effectiveness and the low conservatism of the parameter-dependent and mode-dependent fixed-order filtering method proposed in this paper.     

An improved H∞ filtering for Markovian jump system with time-varying delay based on finite frequency domain

In traditional analysis of system performance, Markovian jump system is often considered in the full frequency domain. However, some unknown factors, such as noise interference, often act on a specific frequency domain, so there is a big defect in putting the system analysis in the full frequency domain. In this paper, the finite frequency domain is introduced into the Markovian jump system. By using generalized KYP lemma, the system is divided into three frequency bands: low, medium and high. The disturbance in different frequency domain is analyzed and the H_∞ filter is designed. In addition, in dealing with inequality relations, the improved Wirtinger inequality method is used, and the Projection lemma is used in dealing with filter coupling terms, and time-varying delay problem in finite frequency domain is also considered. Finally, some examples are given to illustrate the effectiveness of our methods and the specific parameters and convergence graph of the finite frequency domain filter are obtained.     

Robust H∞ persistent dwell time control for switched discrete-time T–S fuzzy systems with uncertainty and time-varying delay

This paper is concerned with the controller synthesis for switched Takagi–Sugeno (T–S) fuzzy systems with time-varying delays, parameter uncertainties and process disturbances. A persistent dwell time (PDT) based control law is mainly proposed for the T–S fuzzy systems in presenting of high-frequency motion switches. Different with the most existing literatures, the dynamics of local subsystems are allowed to be unstable during fast switching time intervals as well as the jump time instants. In addition, the maximal period of persistence time is not limited. Under the influences of the time-varying delays, uncertainties and disturbances, the proposed method ensures the overall closed-loop system to be globally uniformly exponentially stable. Moreover, a pre-given H_∞ performance can be simultaneously guaranteed. Numerical examples are provided to demonstrate the effectiveness of the proposed method.     

Adaptive event-triggered H∞ fuzzy filtering for interval type-2 T–S fuzzy-model-based networked control systems with asynchronously and imperfectly matched membership functions

This paper is concerned with the network-based H_∞ fuzzy filtering for non-linear systems with parameter uncertainties under a novel adaptive discrete event-triggered communication scheme (DETCS). Based on interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy model, the non-linear systems with parameter uncertainties are represented as a class of IT2 T–S fuzzy systems. In the design process, a novel adaptive DETCS is proposed to reduce the usage of system resources and adapt the variation of plant output, and a novel networked IT2 T–S fuzzy filter is applied to improve the flexibility of filter design. By employing the time-delay systems modeling method, the filtering-error-system is modeled as a class of interval time-varying delayed IT2 T–S fuzzy systems with asynchronously and imperfectly matched membership functions, and further conditionally expressed as a favorable form. Then, some relaxed stability criteria are established to determine that this class of delayed IT2 T–S fuzzy systems is asymptotically stable with a prescribed H_∞ disturbance attenuation performance. Also, the co-design of parameter matrices of adaptive DETCS and filter is implemented. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.     

Decentralized event-triggered H∞ control for switched systems with network communication delay

This paper is concerned with the decentralized event-triggered H_∞ control for switched systems subject to network communication delay and exogenous disturbance. Depending on different physical properties, the system state is divided into multiple communication channels and decentralized sensors are employed to collect signals on these channels. Furthermore, decentralized event-triggering mechanisms (DETMs) with a switching structure are proposed to determine whether the sampled data needs to be transmitted. In particular, an improved data buffer is presented which can guarantee more timely utilization of the sampled data. Then, with the proposed DETMs and data buffer, a time-delay closed-loop switched system is developed. After that, sufficient conditions are presented to guarantee the H_∞ performance of the closed-loop switched system by utilizing the average dwell time and piecewise Lyapunov functional method. Since the event-triggered instants and the switching instants may stagger with each other, the influence of their coupling on the H_∞ performance analysis is systematically discussed. Subsequently, sufficient conditions for designing the event-triggered state feedback controller gains are provided. Finally, numerical simulations are given to verify the effectiveness of the proposed method.     

H∞ finite time control for discrete time-varying system with interval time-varying delay

This paper discusses the problem of H_∞ finite time control for a discrete time-varying system with interval time-varying delay. By constructing a new augmented time-varying Lyapunov functional involving triple summation items and using discrete Wirtinger-type inequalities, delay-dependent conditions are derived, which guarantee that the closed-loop system is not only finite time bounded (FTB) but also satisfies an H_∞ performance. Furthermore, the time-varying feedback controller can be derived by solving a series of recursive linear matrix inequalities (RLMIs). Simulation results show the effectiveness and superiority of the proposed method.     

An event-triggered asynchronous H∞ filtering for singular Markov jump systems with redundant channels

In this paper, the problem of asynchronous H_∞ filtering for singular Markov jump systems with redundant channels under the event-triggered scheme is studied. In order to save the resource of bandwidth limited network and improve quality of data transmission, we utilize event-triggered scheme and employ redundant channels. The redundant channels are modeled as two mutually independent Bernoulli distributed random variables. To formulate the asynchronization phenomena between the system modes and the filter modes, the hidden Markov model is proposed so that the filtering error system has become a singular hidden Markov jump system. The criterion of regular, causal and stochastically stable with a certain H_∞ performance for the filtering error system has been obtained. The co-design of asynchronous filter and the event-triggered scheme is proposed in terms of a group of feasible linear matrix inequalities. Two examples are given to show the effectiveness of the proposed method.     

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.     

Robust H∞ filtering for switched stochastic systems under asynchronous switching

This paper investigates the problem of robust H_∞ filtering for switched stochastic systems under asynchronous switching. The so-called asynchronous switching means that the switching between the filters and system modes is asynchronous. The aim is to design a filter ensuring robust exponential mean square stability and a prescribed H_∞ performance level for the filtering error systems. Based on the average dwell time approach and piecewise Lyapunov functional technique, sufficient conditions for the existence of the robust H_∞ filter are derived, and the proposed filter can be obtained by solving a set of LMIs(linear matrix inequalities). Finally, a numerical example is given to show the effectiveness of the proposed approach.     

Delay-dependent H∞ filtering for discrete singular Markov jump systems with Wiener process and partly unknown transition probabilities

This paper is devoted to the investigation of the delay-dependent H_∞ filtering problem for a class of discrete-time singular Markov jump systems with Wiener process and partly unknown transition probabilities. The class of stochastic singular model under consideration is more general and covers the stochastic singular Markov jump time-varying delay systems with completely known and completely unknown transition probabilities as two special cases. Firstly, based on a stochastic Lyapunov–Krasovskii candidate function and an auxiliary vector function, by employing some appropriate free-weighting matrices, the discretized Jensen inequality and combining them with the structural characteristics of the filtering error system, a set of delay-dependent sufficient conditions are established, which ensure that the filtering error system is stochastically admissible. And then, a singular filter is designed such that the filtering error system is not only regular, causal and stochastically stable, but also satisfy a prescribed H_∞ performance for all time-varying delays no larger than a given upper bound. Furthermore, the sufficient conditions for the solvability of the H_∞ filtering problem are obtained in terms of a new type of Lyapunov–Krasovskii candidate function and a set of linear matrix inequalities. Finally, simulation examples are presented to illustrate the effectiveness of the proposed method in the paper.     

Networked H∞ filtering for T–S fuzzy systems with quantization and data dropouts

This paper studies the problem of _H∞$H_{\infty }$ filtering problem for a class of nonlinear time-varying delay systems with unideal communication links. Two defectives are concerned including measurement quantization and packet dropouts. The quantized measurements are transmitted to the filter via network, where the phenomena of packet loss are taken into account. By using Lyapunov–Krasovskii functional, a less conservative delay-dependent stability condition for the closed-loop NCSs is derived. The _H∞$H_{\infty }$ fuzzy controller, which is designed in terms of linear matrix inequalities (LMIs), is developed for the asymptotic stabilization of the closed-loop NCSs. Numerical examples are given to illustrate the effectiveness of the proposed method.     

H∞ control of periodic piecewise polynomial time-varying systems with polynomial Lyapunov function

In this paper, the H_∞ control problem of periodic piecewise systems with polynomial time-varying subsystems is addressed. Based on a periodic Lyapunov function with a continuous time-dependent Lyapunov matrix polynomial, the H_∞ performance is studied. The result can be easily reduced to the conditions for periodic piecewise systems with constant subsystems or linear time-varying systems based on a common Lyapunov function or a linear time-varying Lyapunov matrix. Moreover, an H_∞ controller with time-varying polynomial controller gain is proposed as well, which could be directly solved with the linear matrix inequalities. A numerical example is presented to demonstrate the effectiveness of the proposed method.     

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.