Full-order Filter Research Articles

Enhanced H ∞ filtering for continuous-time state-delayed systems

The H∞ filtering problem for continuous-time polytopic uncertain time-delay systems is investigated. Attention is focused on the design of full-order filters guaranteeing a prescribed H∞ attenuation level for the filtering error system. First, a simple alternative proof is given for an improved linear matrix inequality (LMI) representation of H∞ performance. Then, based on the performance criterion which keeps Lyapunov matrices out of the product of system dynamic matrices, a sufficient condition for the existence of robust estimators is formulated in terms of LMIs, and the corresponding filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical algorithms. It is shown that the proposed design strategy allows the use of parameter-dependent Lyapunov functions and hence it is less conservative than some earlier results. A numerical example is employed to demonstrate the feasibility and advantage of the proposed design.

Mode-dependent [formula omitted] filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities

In this paper, the problem of H ∞ filtering for a class of discrete-time Markovian jump linear systems (MJLS) with partly unknown transition probabilities is investigated. The considered systems are more general, which cover the MJLS with completely known and completely unknown transition probabilities as two special cases. A mode-dependent full-order filter is constructed and the bounded real lemma (BRL) for the resulting filtering error system is derived via LMI formulation. Then, an improved version of the BRL is further given by introducing additional slack matrix variables to eliminate the cross coupling between system matrices and Lyapunov matrices among different operation modes. Finally, the existence criterion of the desired filter is obtained such that the corresponding filtering error system is stochastically stable with a guaranteed H ∞ performance index. A numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results.

Robust [formula omitted] filter design for neutral stochastic uncertain systems with time-varying delay

In this paper, the robust H ∞ filtering problem for a class of neutral stochastic systems is discussed. The system under consideration contains parameter uncertainties, Itô-type stochastic disturbances, time-varying delay. The parameter uncertainties are assumed to be time-varying norm-bounded. Using the stochastic Lyapunov stability theory and Itô's differential rule, a full-order filter is designed for all admissible uncertainties and time-varying delay, which is expressed in the form of linear matrix inequality (LMI). The dynamics of the filtering error systems are guaranteed to be robust stochastically mean square asymptotically stable, while achieving a prescribed stochastic robust H ∞ performance level. At the end of this paper, a numerical example is given to demonstrate the usefulness of the proposed method.

H ∞ Fuzzy Filtering for Discrete-Time Nonlinear Systems via Fuzzy Lyapunov Function Approach

This paper is concerned with the H ? fuzzy filtering problem for a class of discrete-time fuzzy systems. The objective is to design a stable filter guaranteeing the asymptotic stability and a prescribed H ? performance of the filtering error system. Motivated by the parallel distributed compensation (PDC) technique, a new filter model is proposed in this paper. Both full-order and reduced-order filters are established, and they can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired H ? fuzzy filter is given. A numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach.

LMI APPROACH TO ROBUST FILTERING FOR DISCRETE TIME-DELAY SYSTEMS WITH NONLINEAR DISTURBANCES

This paper investigates the problem of robust filtering for a class of uncertain nonlinear discrete-time systems with multiple state delays. It is assumed that the parameter uncertainties appearing in all the system matrices reside in a polytope, and that the nonlinearities entering into both the state and measurement equations satisfy global Lipschitz conditions. Attention is focused on the design of robust full-order and reduced-order filters guaranteeing a prescribed noise attenuation level in an H∞ or l2-l∞ sense with respect to all energy-bounded noise disturbances for all admissible uncertainties and time delays. Both delay-dependent and independent approaches are developed by using linear matrix inequality (LMI) techniques, which are applicable to systems either with or without a priori information on the size of delays.

Robust fault estimation of uncertain systems using an LMI‐based approach

AbstractGeneral recent techniques in fault detection and isolation (FDI) are based on H∞ optimization methods to address the issue of robustness in the presence of disturbances, uncertainties and modeling errors. Recently developed linear matrix inequality (LMI) optimization methods are currently used to design controllers and filters, which present several advantages over the Riccati equation‐based design methods. This article presents an LMI formulation to design full‐order and reduced‐order robust H∞ FDI filters to estimate the faulty input signals in the presence of uncertainty and model errors. Several cases are examined for nominal and uncertain plants, which consider a weight function for the disturbance and a reference model for the faults. The FDI LMI synthesis conditions are obtained based on the bounded real lemma for the nominal case and on a sufficient extension for the uncertain case. The conditions for the existence of a feasible solution form a convex problem for the full‐order filter, which may be solved via recently developed LMI optimization techniques. For the reduced‐order FDI filter, the inequalities include a non‐convex constraint, and an alternating projections method is presented to address this case. The examples presented in this paper compare the simulated results of a structural model for the nominal and uncertain cases and show that a degree of conservatism exists in the robust fault estimation; however, more reliable solutions are achieved than the nominal design. Copyright © 2008 John Wiley & Sons, Ltd.

Formula omitted] filtering for 2D Markovian jump systems

This paper is concerned with the problem of H ∞ filtering for 2D discrete Markovian jump systems. The mathematical model of 2D jump systems is established upon the well-known Roesser model. Our attention is focused on the design of a full-order filter, which guarantees the filtering error system to be mean-square asymptotically stable and has a prescribed H ∞ disturbance attenuation performance. Sufficient conditions for the existence of a desired filter are established in terms of linear matrix inequalities (LMIs), and the corresponding filter design is cast into a convex optimization problem which can be efficiently solved by using commercially available numerical software. A numerical example is provided to illustrate the effectiveness of the proposed design method.

Formula omitted] filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities

In this paper, we deal with the robust H ∞ filtering problem for a class of uncertain nonlinear time-delay stochastic systems. The system under consideration contains parameter uncertainties, Itô-type stochastic disturbances, time-varying delays, as well as sector-bounded nonlinearities. We aim at designing a full-order filter such that, for all admissible uncertainties, nonlinearities and time delays, the dynamics of the filtering error is guaranteed to be robustly asymptotically stable in the mean square, while achieving the prescribed H ∞ disturbance rejection attenuation level. By using the Lyapunov stability theory and Itô’s differential rule, sufficient conditions are first established to ensure the existence of the desired filters, which are expressed in the form of a linear matrix inequality (LMI). Then, the explicit expression of the desired filter gains is also characterized. Finally, a numerical example is exploited to show the usefulness of the results derived.

Robust [formula omitted] filtering for discrete nonlinear stochastic systems with time-varying delay

In this paper, we are concerned with the robust H ∞ filtering problem for a class of nonlinear discrete time-delay stochastic systems. The system under study involves parameter uncertainties, stochastic disturbances, time-varying delays and sector-like nonlinearities. The problem addressed is the design of a full-order filter such that, for all admissible uncertainties, nonlinearities and time delays, the dynamics of the filtering error is constrained to be robustly asymptotically stable in the mean square, and a prescribed H ∞ disturbance rejection attenuation level is also guaranteed. By using the Lyapunov stability theory and some new techniques, sufficient conditions are first established to ensure the existence of the desired filtering parameters. These conditions are dependent on the lower and upper bounds of the time-varying delays. Then, the explicit expression of the desired filter gains is described in terms of the solution to a linear matrix inequality (LMI). Finally, a numerical example is exploited to show the usefulness of the results derived.

Robust L2 - L∞ Filtering for Uncertain Nonlinearly Parameterized Stochastic Systems with Time-Varying Delays

This paper is concerned with the problem of robust L2 - L∞ filtering for uncertain stochastic time-delay systems in the nonlinear fractional transformation (NFT) form. Attention is focused on the design of both full-order and reduced-order filters, guaranteeing robust stochastic stability and a prescribed level of L2 - L∞ performance for the filtering error system. A parameter-dependent Lyapunov functional is employed to solve the problem. The concerned filters are not only parameter dependent but also have the NFT form. Sufficient conditions for the existence of such filters are presented in terms of certain linear matrix inequalities (LMIs). Desired filters are explicitly expressed based on the solutions to the proposed LMIs. A numerical example is provided to demonstrate the effectiveness of the proposed method.

Exponential H∞ filtering for uncertain discrete‐time switched linear systems with average dwell time: A µ‐dependent approach

AbstractIn this paper, the problem of exponential H∞ filter problem for a class of discrete‐time polytopic uncertain switched linear systems with average dwell time switching is investigated. The exponential stability result of the general discrete‐time switched systems using a discontinuous piecewise Lyapunov function approach is first explored. Then, a new µ‐dependent approach is proposed, which means the analysis or synthesis of the underlying systems is dependent on the increase degree µ of the piecewise Lyapunov function at the switching instants. A mode‐dependent full‐order filter is designed such that the developed filter error system is robustly exponentially stable and achieves an exponential H∞ performance. Sufficient existence conditions for the desired filter are derived and formulated in terms of a set of linear matrix inequalities, and consequently the minimal average dwell time and the corresponding filter are obtained from such conditions for a given system decay degree. A numerical example is presented to demonstrate the potential and effectiveness of the developed theoretical results. Copyright © 2007 John Wiley & Sons, Ltd.

Delay-Dependent <formula formulatype="inline"><tex>$H_{\infty }$</tex> </formula> Control and Filtering for Uncertain Markovian Jump Systems With Time-Varying Delays

This paper deals with the problems of delay-dependent robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> control and filtering for Markovian jump linear systems with norm-bounded parameter uncertainties and time-varying delays. In terms of linear matrix inequalities, improved delay-dependent stochastic stability and bounded real lemma (BRL) for Markovian delay systems are obtained by introducing some slack matrix variables. The conservatism caused by either model transformation or bounding techniques is reduced. Based on the proposed BRL, sufficient conditions for the solvability of the robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> control and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> filtering problems are proposed, respectively. Dynamic output feedback controllers and full-order filters, which guarantee the resulting closed-loop system and the error system, respectively, to be stochastically stable and satisfy a prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> performance level for all delays no larger than a given upper bound, are constructed. Numerical examples are provided to demonstrate the reduced conservatism of the proposed results in this paper.

Filtering for uncertain 2-D discrete systems with state delays

This paper is concerned with the problem of robust H ∞ filtering for two-dimensional (2-D) discrete systems with time-delays in states. The 2-D systems under consideration are described in terms of the well-known Fornasini–Marchesini local state-space (FMLSS) models with time-delays. Our attention is focused on the design of a full-order filter such that the filtering error system is guaranteed to be asymptotically stable with a prescribed H ∞ disturbance attenuation performance. Sufficient conditions for the existence of desired filters are established by using a linear matrix inequality (LMI) approach, and the corresponding filter design problem is then cast into a convex optimization problem that can be efficiently solved by resorting to some standard numerical software. Furthermore, the obtained results are extended to more general cases where the system matrices contain either polytopic or norm-bounded parameter uncertainties. A simulation example is provided to illustrate the effectiveness of the proposed design method.

A Fault Detection Filter Including an Adaptive Noise Cancellation Strategy

This paper is concerned with the problem of Fault Detection and Isolation (FDI) in stochastic discretetime dynamic systems. In order to recover the whiteness property of optimal linear filters and the fault isolation property of detection filters, a full-order Kalman filter is designed under a state feedback decoupling constraint. The obtained detection filter includes an adaptive noise cancellation strategy based on the reduced output residuals decoupled from faults. Necessary and sufficient conditions for stability and convergence of the proposed filter are established.

Delay-dependent robust ℋ∞ and ℒ2-ℒ∞ filtering for LPV systems with both discrete and distributed delays

The problems of delay-dependent robust H-infinity and L2-L-infinity filtering for a class of linear parameter varying systems with both discrete and distributed delays is discussed. The distributed delays are assumed to appear in both the state and measurement equations. Attention is focused on the design of delay-dependent robust full-order filters that guarantee the robust asymptotic stability and a prescribed noise attenuation level in an H1 or L2-L1 sense for the filtering error dynamics. The desired filters can be obtained from the solution of convex optimisation problems in terms of linear matrix inequalities that can be solved by efficient interior-point algorithms. A numerical example is included to illustrate the effectiveness of the proposed design methods.

Optimal filtering and smoothing for discrete-time stochastic singular systems

A stochastic singular system with correlated noises at the same time is transferred to the equivalent nonsingular system with correlated noises at the same and neighboring time. Applying time-domain innovation analysis method, the recursive full-order predictor, filter and smoother are presented for this nonsingular system. Further, the full-order filter and smoother are given for original stochastic singular linear systems with correlated noises. Recursive and nonrecursive computational formulas for estimation error covariance matrices are given. Furthermore, the steady-state filter and smoother are also investigated. The asymptotic stability is proved. All results generalize the standard Kalman filtering. A simulation example shows the effectiveness.

Filtering for a class of nonlinear discrete-time stochastic systems with state delays

In this paper, the filtering problem is investigated for a class of nonlinear discrete-time stochastic systems with state delays. We aim at designing a full-order filter such that the dynamics of the estimation error is guaranteed to be stochastically, exponentially, ultimately bounded in the mean square, for all admissible nonlinearities and time delays. First, an algebraic matrix inequality approach is developed to deal with the filter analysis problem, and sufficient conditions are derived for the existence of the desired filters. Then, based on the generalized inverse theory, the filter design problem is tackled and a set of the desired filters is explicitly characterized. A simulation example is provided to demonstrate the usefulness of the proposed design method.

H∞ filtering on nonlinear stochastic systems with delay

Abstract This paper is concerned with the problem of H ∞ filtering for a class of nonlinear Ito stochastic systems with delay. The objective is to design such a full-order filter that the L 2 gain from the exogenous input to an estimation error is minimized or guaranteed to be less or equal to a prescribed value. Sufficient conditions are obtained for the existence of desired H ∞ filters, which are given in terms of the solutions to quadratic matrix inequalities involving scalar parameters. A numerical example is provided to demonstrate the effectiveness of the proposed approach.

ON THE DESIGN OF HIGH-ORDER ROBUST LINEAR H∞ FILTERS FOR A CLASS OF UNCERTAIN NONLINEAR SYSTEMS

This paper addresses the design of robust linear H∞ filters for a class of nonlinear systems subject to uncertain, possibly time-varying, parameters. The nonlinear system is described by a differential-algebraic representation, which can model the whole class of systems with rational functions of the state and uncertain parameters, as well as some trigonometric nonlinearities. The admissible values of the uncertain parameters and their rate of variation are assumed to belong to a given polytope. A linear matrix inequality (LMI) method is presented to design full-order robust linear filters with a minimized upper-bound on the &ℒ2-gain of the noise-to-estimation error operator for all admissible uncertainty. An LMI procedure based on the latter method is then developed to obtain high-order robust linear filters, which are shown, via an example, to achieve significant performance improvement over the full-order filter.

H2 Optimal Robust Filtering

In this paper, a design procedure for H 2 optimal robust filtering is presented. The robust filter is determined from the equilibrium solution of a minimax programming problem where the H 2 norm of the estimation error is maximized with respect to the feasible uncertainties and minimized with respect to all full order, linear, rational and causal filters. As the main contribution, it is shown that for the class of parameter uncertainty considered, the equilibrium solution of the aforementioned minimax problem can be exactly determined. In contrast to the design methods available in the literature to date, dealing with norm bounded or convex bounded parameter uncertainty, which naturally provide suboptimal solutions to the robust filtering problem, the one presented in this paper does not present any degree of conservatism due to the particular parameter uncertainty model taken into consideration. However, the price to be payed to reach robust optimality is that the order of the optimal robust filter is, in general, very high. The classical static linear approximation problem as well as the filter design problem corresponding to continuous and discrete time linear systems are considered. In the last section, an illustrative example is presented to make clear the main features of the reported results.