Filtering Error System Research Articles

L2–L∞ filtering for stochastic systems driven by Poisson processes and Wiener processes

This paper investigates the L2–L∞ filtering problem for stochastic systems driven by Poisson processes and Wiener processes. Firstly, this paper presents an approach to transform the expectation of stochastic integral with respect to Poisson process into the expectation of Lebesgue integral by the martingale theory. Then, based on this, a filter is designed to guarantee that the filtering error system is mean-square asymptotically stable and its L2–L∞ performance satisfies a prescribed level. Finally, a simulation example is given to illustrate the effectiveness of the proposed filtering scheme.

Positive Filtering withl1-Gain for Discrete-Time Positive Systems

This paper is concerned with the positive filtering problem for discrete-time positive systems under thel1-induced performance. We aim to propose a pair of positive filters with error-bounding features to estimate the output of positive systems. A novel characterization is first constructed so that the filtering error system is asymptotically stable with a prescribedl1-induced performance. Then, necessary and sufficient conditions for the existence of required filters are presented, and the obtained results are expressed as linear programming problems. Moreover, it is pointed out that the results can be easily checked by standard software. In addition, a numerical example is given to show the effectiveness of the proposed design procedures.

Energy-Efficient Distributed Filtering in Sensor Networks: A Unified Switched System Approach.

This paper is concerned with the energy-efficient distributed filtering in sensor networks, and a unified switched system approach is proposed to achieve this goal. For the system under study, the measurement is first sampled under nonuniform sampling periods, then the local measurement elements are selected and quantized for transmission. Then, the transmission rate is further reduced to save constrained power in sensors. Based on the switched system approach, a unified model is presented to capture the nonuniform sampling, the measurement size reduction, the transmission rate reduction, the signal quantization, and the measurement missing phenomena. Sufficient conditions are obtained such that the filtering error system is exponentially stable in the mean-square sense with a prescribed H∞ performance level. Both simulation and experiment studies are given to show the effectiveness of the proposed new design technique.

Robust filtering for Markovian jump neutral systems with distributed delays

ABSTRACTOver the past decades, a great deal of attention has been devoted to parameter-invariant neutral systems. However, in practical applications, the jump of parameters frequently occurs to neutral systems on account of sudden environmental changes, which can be described by Markovian jump systems. This paper mainly deals with the problem of robust filtering for uncertain Markovian jump neutral systems with distributed delays. The uncertain parameters are assumed to be time varying and norm bounded. By utilizing the Newton–Leibniz formula and integral inequality technique, the delay-dependent sufficient conditions for the existence of the filter are derived such that the filtering error system is stochastically stable with an performance constraint. Based on the obtained criteria and by employing congruent transformation, the robust filter is designed in terms of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.

Event-Triggered Generalized Dissipativity Filtering for Neural Networks With Time-Varying Delays.

This paper is concerned with event-triggered generalized dissipativity filtering for a neural network (NN) with a time-varying delay. The signal transmission from the NN to its filter is completed through a communication channel. It is assumed that the network measurement of the NN is sampled periodically. An event-triggered communication scheme is introduced to design a suitable filter such that precious communication resources can be saved significantly while certain filtering performance can be ensured. On the one hand, the event-triggered communication scheme is devised to select only those sampled signals violating a certain threshold to be transmitted, which directly leads to saving of precious communication resources. On the other hand, the filtering error system is modeled as a time-delay system closely dependent on the parameters of the event-triggered scheme. Based on this model, a suitable filter is designed such that certain filtering performance can be ensured, provided that a set of linear matrix inequalities are satisfied. Furthermore, since a generalized dissipativity performance index is introduced, several kinds of event-triggered filtering issues, such as H∞ filtering, passive filtering, mixed H∞ and passive filtering, (Q,S,R) -dissipative filtering, and L2 - L∞ filtering, are solved in a unified framework. Finally, two examples are given to illustrate the effectiveness of the proposed method.

Robust Finite-Time <em>H</em><sub><em>∞</em></sub> Filtering for Itô Stochastic Systems

This paper investigates the problem of robust finite-time H∞ filter design for Ito stochastic systems. Based on linear matrix inequalities (LMIS) techniques and stability theory of stochastic differential equations, stochastic Lyapunov function method is adopted to design a finite-time H∞ filter such that, for all admissible uncertainties, the filtering error system is stochastic finite-time stable (SFTS). A sufficient condition for the existence of a finite-time H∞ filter for the stochastic system under consideration is achieved in terms of LMIS. Moreover, the explicit expression of the desired filter parameters is given. A numerical example is provided to illustrate the effectiveness of the proposed method.

Resilient H∞ filtering for discrete-time uncertain Markov jump neural networks over a finite-time interval

In this paper, the resilient finite-time H∞ filtering problem for discrete-time uncertain Markov jump neural networks with packet dropouts is investigated. The purpose is to design a filter which is insensitive with respect to filter gain uncertainties subjects to an H∞ performance level. The data packet dropouts phenomenon modeled by a stochastic Bernoulli distributed process is also considered. In terms of the linear matrix inequalities methodology, some sufficient conditions which guarantee that the filtering error system is finite-time bounded with a prescribed H∞ performance level are established. Based on the conditions, an explicit expression for the desired filter is given. A numerical example is provided to illustrate the validness of the proposed scheme.

Energy‐efficient distributed control of large‐scale systems: A switched system approach

SummaryThis paper is concerned with the sensor‐network‐based distributed control of large‐scale systems with the power constraint. In the underlying system, the measurement is firstly sampled under nonuniform sampling periods, which are varying in a given set. Then, the measurement size reduction technique and communication rate reduction method are used to save the constrained power in sensor networks. Specifically, only one element of sampled measurement is chosen at each sampling time instant, and it is then quantized and transmitted to the neighbouring controllers. Based on the switched system approach, a unified model is presented to capture the nonuniform sampling, the measurement size reduction, the transmission rate reduction and the controller failure phenomenon. A new sufficient condition is obtained such that the filtering error system is exponentially stable in the mean‐square sense with a prescribed H∞ performance level. Based on this condition, the controller gains are designed by using the cone complementarity linearization algorithm. Finally, a simulation study is given to show the effectiveness of the proposed new design technique. Copyright © 2015 John Wiley & Sons, Ltd.

Finite-Time $H_{\infty }$ Filtering for T–S Fuzzy Discrete-Time Systems With Time-Varying Delay and Norm-Bounded Uncertainties

In this paper, we investigate the filtering problem of discrete-time Takagi–Sugeno (T–S) fuzzy uncertain systems subject to time-varying delays. A reduced-order filter is designed. With the augmentation technique, a filtering error system with delayed states is obtained. In order to deal with time delays in system states, the filtering error system is first transformed into two interconnected subsystems. By using a two-term approximation for the time-varying delay, sufficient delay-dependent conditions of finite-time boundedness and $H_{\infty }$ performance of the filtering error system are derived with the Lyapunov function. Based on these conditions, the filter design methods are proposed and the filter gain matrices can be obtained by calculating a set of linear matrix inequalities. A numerical example is used to illustrate the effectiveness of the proposed approaches.

Passive filter design for periodic stochastic systems with quantized measurements and randomly occurring nonlinearities

In this paper, the passive filter is designed for periodic stochastic systems with quantized measurements and randomly occurring nonlinearities. According to the dynamic properties of periodic systems, an N-periodic density quantizer is proposed to make full use of the communication capacity. By using Bernoulli processes, a new model is introduced to describe the randomly occurring nonlinearities, where each component of the state appears nonlinearity independently, and they influence each other based on the coupling matrices B(k). A reduced-order filter is designed to reduce the computation burden. Then sufficient conditions are established to ensure that the filtering error system is stochastically stable and satisfies the passivity. Finally, the effectiveness of the proposed new design technique is illustrated via a numerical example.

Non-fragile distributed filtering for fuzzy systems with multiplicative gain variation

This paper is concerned with the non-fragile distributed H∞ filtering problem for a class of discrete-time Takagi–Sugeno (T–S) systems with multiplicative gain variation. The multiplicative gain uncertainties reflecting the imprecision of the filter implementation are firstly described. Based on the fuzzy Lyapunov functional approach, a sufficient condition is presented such that the filtering error system is asymptotically stable with a prescribed H∞ performance level. The filter gain parameters are determined by solving an optimization problem. Application on the robotic manipulator is given to show the effectiveness of the proposed new design method.

New results onH∞filtering for nonlinear large-scale systems with interconnected time-varying delays

Summary This paper proposes a new design method of H∞ filtering for nonlinear large-scale systems with interconnected time-varying delays. The interaction terms with interval time-varying delays are bounded by nonlinear bounding functions including all states of the subsystems. A stable linear filter is designed to ensure that the filtering error system is exponentially stable with a prescribed convergence rate. By constructing a set of improved Lyapunov functions and using generalized Jensen inequality, new delay-dependent conditions for designing H∞ filter are obtained in terms of linear matrix inequalities. Finally, an example is provided to illustrate the effectiveness of the proposed result. Copyright © 2015 John Wiley & Sons, Ltd.

Energy-efficient [formula omitted] filtering over wireless networked systems—A Markovian system approach

This paper is concerned with the energy-efficient filtering over wireless networked systems, and a Markovian system approach is proposed to achieve this goal. Firstly, the local measurement is stochastically sampled under nonuniform sampling periods, then the measurement size reduction scheme is applied and only one element of measurement is stochastically selected for quantization. Then, a stochastic transmission protocol is introduced to further save power. Based on the Markovian system approach, a new model is presented for the nonuniform sampling, the measurement size reduction, the signal quantization and the stochastic signal transmission. Sufficient conditions are obtained such that the filtering error system is exponentially stable in the mean-square sense with a prescribed H∞ performance level. A simulation study is given to show the effectiveness of the proposed new design technique.

Non-fragile filtering for fuzzy stochastic systems over fading channel

This paper investigates the problem of non-fragile filter design for nonlinear stochastic systems subject to channel fading. The nonlinear stochastic systems are represented by the Takagi–Sugeno (T–S) model and the channel fading is described by a random process. By using the Lyapunov method, a sufficient condition which guarantees that the filtering error system is stochastically stable and satisfies the passive performance is established. Then the parameters of the non-fragile filter are obtained by solving linear matrix inequalities (LMIs). Finally, numerical examples are employed to illustrate the effectiveness of the proposed approach.

Fuzzy Filtering for a Class of Nonlinear Systems with Feedback Uncertainties

This paper studies the problem of $$H_\infty $$ filtering for nonlinear uncertain systems. The parameter uncertainties are assumed to be a class of feedback uncertainties. The nonlinear plant is represented by a Takagi–Sugeno fuzzy model. The paper is focused on the design of a fuzzy filter guaranteeing a prescribed $$H_\infty $$ performance of the filtering error system. By introducing some slack matrix variables, a sufficient condition for the $$H_\infty $$ filter design is presented in terms of solutions to a set of linear matrix inequalities. A simulation example will be given to show the efficiency of the proposed method.

Dissipativity-based filtering of nonlinear periodic Markovian jump systems: The discrete-time case

This paper is concerned with the problem of dissipative filtering for discrete-time periodic Markovian jump systems with bounded nonlinearity. It is assumed that the data measurements from the plant to the filter are subject to randomly occurred packet dropouts satisfying Bernoulli distribution. The purpose of this paper is to design a filter such that the filtering error system is stochastically stable and strictly (Q,S,R)-dissipative. To eliminate the cross coupling between the Lyapunov matrix and system matrices, some slack matrix variables are introduced. Based on a mode-dependent and basis-dependent Lyapunov function, a sufficient condition of the desired dissipative filter in terms of linear matrix inequalities (LMIs) for discrete-time Periodic Markovian Jump Systems with bounded nonlinearity is derived. Finally, a numerical example is exploited to demonstrate the effectiveness of the proposed filter design method.

Nonfragile H∞ filtering for wireless‐networked systems with energy constraint

This article is concerned with the nonfragile filtering for wireless‐networked systems with energy constraint. To achieve the energy‐efficient goal, the local measurement is first sampled by nonuniform sampling, then we only choose one measurement to transmit it to the remote filter. In the filter design, the random occurring filter gain variation problem is taken into account. A new stochastic switched system model is presented to capture the nonuniform sampling, the measurement size reduction, and the random filter gain phenomena. Based on the switched system approach, stochastic system analysis, and Lyapunov stability theory, a sufficient condition is presented such that the filtering error system is exponentially stable in the mean‐square sense and a prescribed performance level is also guaranteed. The effectiveness of the proposed new method is illustrated by a simulation example. © 2015 Wiley Periodicals, Inc. Complexity 21: 79–89, 2016

Delay-Dependent Robust Dissipative Filter for T-S Fuzzy Descriptor Time-Varying Delay Systems

This paper deals with the delay-dependent robust dissipative filter for a class of T-S fuzzy descriptor systems with parameter uncertainties. Based on Lyapunov stability theory, sufficient conditions on the existence of robust dissipative filters is derived, which guarantee that the filter error system is asymptotically stable with a dissipative index. And the design of a delay-dependent filter can be obtained by solving the linear matrix inequalities. Finally, numerical examples are given to illustrate the effectiveness and superiority of the obtained results.

New Results on Decentralized $${\fancyscript{H}}_{\infty }$$ H ∞ Fuzzy Filtering Design for Continuous-Time Large-Scale Nonlinear Systems with Time-Varying Delay

This paper studies the problem of decentralized $${\fancyscript{H}}_{\infty }$$H? fuzzy filtering design for a class of continuous-time large-scale nonlinear systems with time-varying delay. The considered large-scale system consists of several nonlinear subsystems with interconnections and state delays. Each nonlinear subsystem is represented by a Takagi---Sugeno (T---S) model, and the state delay of each subsystem is assumed to be of an interval-like time-varying form. Attention is focused on designing a decentralized fuzzy filter such that the resulting filtering error system is asymptotically stable with a guaranteed $${\fancyscript{H}}_{\infty }$$H? disturbance attenuation level. We firstly propose a two-term approximation method to transform the filtering error system into an interconnected formulation and reformulate the problem of decentralized $${\fancyscript{H}}_{\infty }$$H? fuzzy filtering design in the context of input---output (IO) stability. Then, based on a Lyapunov---Krasovskii functional (LKF) combined with the scaled small gain (SSG) theorem, less conservative results are presented for the decentralized $${\fancyscript{H}}_{\infty }$$H? fuzzy filtering design in terms of linear matrix inequalities (LMIs). Finally, two examples are provided to illustrate the effectiveness of the proposed method.

Energy Efficient Distributed Filtering for a Class of Nonlinear Systems in Sensor Networks

In this paper, the distributed filtering problem is investigated for a class of nonlinear systems in the wireless sensor networks. The main goal is to design a set of distributed filters and simultaneously to prolong the lifetime of networks. In order to save limited power in sensors, signal quantization is employed to reduce packet size, where the robust control approach is used to handle the quantization error. Then, the communication rate change is allowed and treated under a switched system model. Sufficient conditions are derived such that the filtering error system is exponentially stable in the mean-square sense and achieves a prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance level. The filter parameters are determined by solving an optimization problem. Finally, the effectiveness of the proposed results is demonstrated by two numerical examples.