Delay-dependent decentralized H_∞ filtering for uncertain interconnected systems

This article considers delay dependent decentralized H∞ filtering for a class of uncertain interconnected systems, where the uncertainties are assumed to be time varying and satisfy the norm-bounded conditions. First, combining the Lyapunov-Krasovskii functional approach and the delay integral inequality of matrices, a sufficient condition of the existence of the robust decentralized H∞ filter is derived, which makes the error systems asymptotically stable and satisfies the H∞ norm of the transfer function from noise input to error output less than the specified up-bound on the basis of the form of uncertainties. Then, the above sufficient condition is transformed to a system of easily solvable LMIs via a series of equivalent transformation. Finally, the numerical simulation shows the efficiency of the main results.

Robust H_∞ filtering for discrete-time systems with Markovian switching and time-delays

The robust H∞ filtering problem for uncertain discrete-time Markovian jump linear systems with mode- dependent time-delays is investigated. Attention is focused on designing a Markovian jump linear filter that ensures robust stochastic stability while achieving a prescribed H∞ performance level of the resulting filtering error system, for all admissible uncertainties. The key features of the approach include the introduction of a new type of stochastic Lyapunov functional and some free weighting matrix variables. Sufficient conditions for the solvability of this problem are obtained in terms of a set of linear matrix inequalities. Numerical examples are provided to demonstrate the reduced conservatism of the proposed approach.

Delay-dependent Non-fragile H_∞ Filtering for Uncertain Fuzzy Systems Based on Switching Fuzzy Model and Piecewise Lyapunov Function

This paper is concerned with the non-fragile H∞ filter design problem for uncertain discrete-time Takagi-Sugeno （T-S） fuzzy systems with time delay. To begin with, the T-S fuzzy system is transformed to an equivalent switching fuzzy system. Then, based on the piecewise Lyapunov function and matrix decoupling technique, a new delay-dependent non-fragile H∞ filtering method is proposed for the switching fuzzy system. The proposed condition is less conservative than the previous results. Since only a set of LMIs is involved, the filter parameters can be solved directly. Finally, a design example is provided to illustrate the validity of the proposed method.

Network-Based H_∞ Filtering for Linear Systems with Randomly Varying Sensor Delay

An H∞ filter design for linear time delay system with randomly varying sensor delay is investigated.The delay considered here is assumed to satisfy a certain stochastic characteristic.A stochastic variable satisfying Bernoulli random binary distribution is introduced and a new system model is established by employing the measurements with random delay.By using the linear matrix inequality(LMI) technique,sufficient conditions are derived for ensuring the mean-square stochastic stability of the filtering error systems and guaranteeing a prescribed H∞ filtering performance.Finally,a numerical example is given to demonstrate the effectiveness of the proposed approach.

Neural network-based H∞ filtering for nonlinear systems with time-delays

A novel H∞ design methodology for a neural network-based nonlinear filtering scheme is addressed. Firstly, neural networks are employed to approximate the nonlinearities. Next, the nonlinear dynamic system is represented by the mode-dependent linear difference inclusion （LDI）. Finally, based on the LDI model, a neural network-based nonlinear filter （NNBNF） is developed to minimize the upper bound of H∞ gain index of the estimation error under some linear matrix inequality （LMI） constraints. Compared with the existing nonlinear filters, NNBNF is time-invariant and numerically tractable. The validity and applicability of the proposed approach are successfully demonstrated in an illustrative example.

Robust H_∞ filtering for discrete-time impulsive systems with uncertainty

This paper investigates robust filter design for linear discrete-time impulsive systems with uncertainty under H∞ performance. First, an impulsive linear filter and a robust H∞ filtering problem are introduced for a discrete-time impulsive systems. Then, a sufficient condition of asymptotical stability and H∞ performance for the filtering error systems are provided by the discrete-time Lyapunov function method. The filter gains can be obtained by solving a set of linear matrix inequalities （LMIs）. Finally, a numerical example is presented to show effectiveness of the obtained result.

Nonlinear H_∞ filtering for interconnected Markovian jump systems

The problem of nonlinear H∞ filtering for interconnected Markovian jump systems is discussed. The aim of this note is the design of a nonlinear Markovian jump filter such that the resulting error system is exponentially meansquare stable and ensures a prescribed H∞ performance. A sufficient condition for the solvability of this problem is given in terms of linear matrix inequalities（LMIs）. A simulation example is presented to demonstrate the effectiveness of the proposed design approach.

Robust H_∞ filtering for neutral jump system with time-delays and uncertainties

The problem of robust H∞ filtering for a class of neutral jump systems with time-delay and norm- bounded uncertainties is considered. By re-constructing the system, the dynamics of overall augmented error systems is obtained which involves unknown inputs represented by disturbances, model uncertainties and time-delays. As to the nominal system, sufficient conditions are provided for the existence of the mode-dependent H∞ filter by selecting the appropriate Lyapunov-Krasovskii function and the robust H∞ filter is proposed for the jump system while considering the time-delays and uncertainties. Both of above conditions for the existence of the H∞ filter and roust H∞ filter are presented in terms of linear matrix inequalities, and convex optimization problems are formulated to design the desired filters. By employing the proposed mode-dependent H∞ filter, the systems have the stochastic stability and better ability of restraining disturbances stochastically, and the given prescribed H∞ performance is guaranteed. Simulation resuhs illustrate the effectiveness of developed techniques.

Krein space approach to robust H_∞ filtering for linear uncertain systems

A novel Krein space approach to robust H∞ filtering for linear uncertain systems is developed. The parameter uncertainty, entering into both states and measurement equations, satisfies an energy-type constraint. Then a Krein space approach is used to tackle the robust H∞ filtering problem. To this end, a new Krein space formal system is designed according to the original sum quadratic constraint （SQC） without introducing any nonzero factors into it and, consequently, the estimate recursion is obtained through the filter gain in Krein space. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.

Improved Parameter-dependent H_∞ Filtering for Polytopic Delta Operator Systems

The problem of H∞ filtering for polytopic Delta operator linear systems is investigated. An improved H∞ performance criterion is presented based on the bounded real lemma. Upon the improved performance criterion, a sufficient condition for the existence of parameter-dependent H∞ filtering is derived in terms of linear matrix inequalities. The designed filter can be obtained from the solution of a convex optimization problem. The filter design makes full use of the parameter-dependent approach, which leads to a less conservative result than conventional design methods. A numerical example is given to illustrate the effectiveness of the proposed approach.

New algorithm for robust H_2/H_∞ filtering with error variance assignment

We consider the robust H 2/H ∞ filtering problem for linear perturbed systems with steadystate error variance assignment. The generalized inverse technique of matrix is introduced, and a new algorithm is developed. After two Riccati equations are solved, the filter can be obtained directly, and the following three performance requirements are simultaneously satisfied: The filtering process is asymptotically stable; the steadystate variance of the estimation error of each state is not more than the individual prespecified upper bound; the transfer function from exogenous noise inputs to error state outputs meets the prespecified H ∞ norm upper bound constraint. A numerical example is provided to demonstrate the flexibility of the proposed design approach.

Distributed H_∞ fusion filter design for INS/WSN integrated positioning system

In order to keep stable navigation accuracy when the blind node （BN） moves between two adjacent clusters, a distributed fusion method for the integration of the inertial navigation system （INS） and the wireless sensor network （WSN） based on H∞ filtering is proposed. Since the process and measurement noise in the integration system are bounded and their statistical characteristics are unknown, the H∞ filter is used to fuse the information measured from local estimators in the proposed method. Meanwhile, the filter can yield the optimal state estimate according to certain information fusion criteria. Simulation results show that compared with the federal Kalman solution, the proposed method can reduce the mean error of position by about 45% and the mean error of velocity by about 85 %.

Comparison of robust H_∞ filter and Kalman filter for initial alignment of inertial navigation system

There are many filtering methods that can be used for the initial alignment of an integrated inertial navigation system. This paper discussed the use of GPS, but focused on two kinds of filters for the initial alignment of an integrated strapdown inertial navigation system (SINS). One method is based on the Kalman filter (KF), and the other is based on the robust filter. Simulation results showed that the filter provides a quick transient response and a little more accurate estimate than KF, given substantial process noise or unknown noise statistics. So the robust filter is an effective and useful method for initial alignment of SINS. This research should make the use of SINS more popular, and is also a step for further research.

Distributed H2/H∞ Filter Design for Discrete-Time Switched Systems

This paper addresses an infinite horizon distributed H2/H∞ filtering for discrete-time systems under conditions of bounded power and white stochastic signals. The filter algorithm is designed by computing a pair of gains namely the estimator and the coupling. Herein, we implement a filter to estimate unknown parameters such that the closed-loop multi-sensor accomplishes the desired performances of the proposed H2 and H∞ schemes over a finite horizon. A switched strategy is implemented to switch between the states once the operation conditions have changed due to disturbances. It is shown that the stability of the overall filtering-error system with H2/H∞ performance can be established if a piecewise-quadratic Lyapunov function is properly constructed. A simulation example is given to show the effectiveness of the proposed approach.

H_-/H_∞ fault detection filter design for interval time-varying delays switched systems

The problem of the robust fault detection filter design for time-varying delays switched systems is considered in the framework of mixed H-/H∞. Firstly, the weighted H∞ performance index is utilized as the robustness performance, and the H- index is used as the sensitivity performance for obtaining the robust fault detection filter. Then a novel multiple Lyapunov-Krasovskii function is proposed for deriving sufficient existence conditions of the robust fault detection filter based on the average dwell time technique. By introducing slack matrix variable, the coupling between the Lyapunov matrix and system matrix is removed, and the conservatism of results is reduced. Based on the robust fault detection filter, residual is generated and evaluated for detecting faults. In addition, the results of this paper are dependent on time delays,and represented in the form of linear matrix inequalities. Finally,the simulation example verifies the effectiveness of the proposed method.

H_∞ deconvolution filter design for time-delay linear continuous-time systems

Proposes an H_∞ deconvolution design for time-delay linear continuous-time systems. We first analyze the general structure and innovation structure of the H_∞ deconvolution filter. The deconvolution filter with innovation structure is made up of an output observer and a linear mapping, where the latter reflects the internal connection between the unknown input signal and the output estimate error. Based on the bounded real lemma, a time domain design approach and a sufficient condition for the existence of deconvolution filter are presented. The parameterization of the deconvolution filter can be completed by solving a Riccati equation. The proposed method is useful for the case that does not require statistical information about disturbances. At last, a numerical example is given to demonstrate the performance of the proposed filter.

A novel robust approach for SLAM of mobile robot

The task of simultaneous localization and mapping （SLAM） is to build environmental map and locate the position of mobile robot at the same time. FastSLAM 2.0 is one of powerful techniques to solve the SLAM problem. However, there are two obvious limitations in FastSLAM 2.0, one is the linear approximations of nonlinear functions which would cause the filter inconsistent and the other is the ＂particle depletion＂ phenomenon. A kind of PSO ＆ Hjj-based FastSLAM 2.0 algorithm is proposed. For maintaining the estimation accuracy, H~ filter is used instead of EKF for overcoming the inaccuracy caused by the linear approximations of nonlinear functions. The unreasonable proposal distribution of particle greatly influences the pose state estimation of robot. A new sampling strategy based on PSO （particle swarm optimization） is presented to solve the ＂particle depletion＂ phenomenon and improve the accuracy of pose state estimation. The proposed approach overcomes the obvious drawbacks of standard FastSLAM 2.0 algorithm and enhances the robustness and efficiency in the parts of consistency of filter and accuracy of state estimation in SLAM. Simulation results demonstrate the superiority of the proposed approach.

H_∞ FILTERING FOR CONTINUOUS-TIME SYSTEMS WITH POINTWISE TIME-VARYING DELAY

The problem of H∞ filtering for continuous-time systems with pointwise time-varying delay is investigated in this paper. By applying an innovation analysis in Krein space, a necessary and sufficient condition for the existence of an H∞ filter is derived in two methods： One is the partial differential equation approach, the other is the reorganized innovation analysis approach. The former gives a solution to the proposed H∞ filtering problem in terms of the solution of a partial differential equation with boundary conditions. The later gives an analytical solution to the proposed H∞ filtering problem in terms of the solutions of Riccati and matrix differential equations.

Improved H_∞ filtering for Markov jumping linear systems with non-accessible mode information

This paper is concerned with the H∞ filtering problems for both continuous- and discrete-time Markov jumping linear systems （MJLS） with non-accessible mode information. A new design method is proposed, which greatly reduces the overdesign introduced in the derivation process. The desired filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities （LMIs）, which can be solved via efficient interior-point algorithms. Numerical examples are provided to illustrate the advantages of the proposed approach.