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 H∞ Filtering For Uncertain Stochastic Time‐Delay Systems

This paper deals with the problem of robust H_∞ filtering for uncertain stochastic systems. The system under consideration is subject to time‐varying norm‐bounded parameter uncertainties and unknown time delays in both the state and measurement equations. The problem we address is the design of a stable filter that ensures the robust stochastic stability and a prescribed H_∞ performance level for the filtering error system irrespective of all admissible uncertainties and time delays. A suffient condition for the solvability of this problem is proposed and a linear matrix inequality approach is developed for the design of the robust H_∞ filters. An illustrative example is provided to demonstrate the effctiveness of the proposed approach.     

Exact,almost and optimal input decoupled (delayed) observers

The core of this paper deals with the construction of input-decoupled observers which seek asymptotic estimation of a desired output variable (a linear combination of state and input) of a time-invariant either continuous- or discrete-time system driven by unknown inputs and disturbances. Exact, almost, optimal (suboptimal) and constrained optimal estimation or filtering problems are formulated and studied. All the problems defined and studied here are inherently interconnected, and have a strong common thread of estimation and filtering in the face of the unknown input and external disturbance signals. They are interconnected from a variety of angles, e.g. they are motivated by one another, methods of obtaining the solvability conditions and their methods of solution rely on one another, etc. Thus, a hierarchy of problems and their solutions is built on top of one another. Some of the problems studied here are known in the literature but not in as general a form as is given here, while a majority of the problems studied here are new. A classical variation of all the above problems is also studied here by introducing an l-step delay in estimating the desired output from the measured output. The underlying philosophy throughout this work has been to study most if not all of the facets of estimation and filtering in one stretch under a single folder. Our study of all the above problems has been guided by three important perspectives: (1) obtaining the solvability conditions, both necessary and sufficient; (2) obtaining optimal performance whenever it applies; and (3) developing sound methodologies to design and construct appropriate observers or filters.     

Robust H∞ control for uncertain discrete‐time stochastic bilinear systems with Markovian switching

This paper is concerned with the problems of robust stochastic stabilization and robust H_∞ control for uncertain discrete‐time stochastic bilinear systems with Markovian switching. The parameter uncertainties are time‐varying norm‐bounded. For the robust stochastic stabilization problem, the purpose is the design of a state feedback controller which ensures the robust stochastic stability of the closed‐loop system irrespective of all admissible parameter uncertainties; while for the robust H_∞ control problem, in addition to the robust stochastic stability requirement, a prescribed level of disturbance attenuation is required to be achieved. Sufficient conditions for the solvability of these problems are obtained in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, explicit expressions of the desired state feedback controllers are also given. An illustrative example is provided to show the effectiveness of the proposed approach. Copyright © 2005 John Wiley & Sons, Ltd.     

Optimal‐switched extended H∞ filter for nonlinear systems with stochastic uncertainties

The extended H_∞ filter (EH_∞F) is a conservative solution with infinite‐horizon robustness for the state estimation problem regarding nonlinear systems with stochastic uncertainties, which leads to excessive costs in terms of filtering optimality and reduces the estimation precision, particularly when uncertainties related to external disturbances and noise appear intermittently. In order to restore the filtering optimality lost due to the conservativeness of the EH_∞F design, we developed an optimal‐switched (OS) filtering mechanism based on the standard EH_∞F to obtain an optimal‐switched extended H_∞ filter (OS‐EH_∞F). The OS mechanism has an error‐tolerant switched (ETS) structure, which switches the filtering mode between optimal and H_∞ robust by setting a switching threshold with redundancy to uncertainties, and a robustness‐optimality cost function (ROCF) is introduced to determine the threshold and optimize the ETS structure online. The ROCF is the weighted sum of the quantified filtering robustness and optimality. When a weight is given, the proposed OS‐EH_∞F can obtain the optimal state estimates while maintaining the filtering robustness at an invariant ratio. A simulation example of space target tracking has demonstrated the superior estimation performance of the OS‐EH_∞F compared with some other typical filters, thereby verifying the effectiveness of using the weight to evaluate the estimation result of the filters.     

Nonlinear almost disturbance decoupling

The L₂-gain almost disturbance decoupling problem for SISO nonlinear systems is formulated. Sufficient conditions are identified for the existence of a parametrized state feedback controller such that the L₂-gain from disturbances to output can be made arbitrarily small by increasing its gain. The controller is explicity constructed using a Lyapunov-based recursive scheme. Sufficient conditions for the solvability of the almost disturbance decoupling problem and the explicit construction of teh controller are given for a more restrictive class of nonlinear systems.     

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

General 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.     

STABILIZATION AND H∞ CONTROL FOR UNCERTAIN STOCHASTIC TIME‐DELAY SYSTEMS VIA NON‐FRAGILE CONTROLLERS

This paper considers the problems of robust non‐fragile stochastic stabilization and H_∞ control for uncertain time‐delay stochastic systems with time‐varying norm‐bounded parameter uncertainties in both the state and input matrices. Attention is focused on the design of memoryless state feedback controllers which are subject to norm‐bounded uncertainties. For both the cases of additive and multiplicative controller uncertainties, delay‐independent sufficient conditions for the solvability of the above problems are obtained. The desired state feedback controller can be constructed by solving a certain linear matrix inequality.     

Design of robust non‐fragile H∞ filters for uncertain neutral stochastic systems with distributed delays

This paper deals with the problem of robust non‐fragile H_∞ filtering for neutral stochastic systems with distributed delays and norm‐bounded parameter uncertainties. Attention is focused on the design of a filter which is subject to gain variations, such that the filtering error system is robustly stochastically stable with a prescribed H_∞ performance level for all admissible uncertainties. A delay‐dependent sufficient condition for the solvability of this problem is obtained in terms of a linear matrix inequality. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Composite disturbance‐observer‐based control and H∞ control for complex continuous models

A novel type of control scheme combining the disturbance‐observer‐based control (DOBC) with H_∞ control is proposed for a class of complex continuous models with disturbances. The disturbances are supposed to include two parts. One part in the input channel is generated by an exogenous system with uncertainty, which can represent the harmonic signals with modeling perturbations. The other part is supposed to have the bounded H₂‐norm. Parametric uncertainties exist both in concerned plant and in exogenous subsystem. The disturbance observers based on regional pole placement and D‐stability theory are designed and integrated with conventional H_∞ control laws. The new composite DOBC and H_∞ control scheme is applied to complex continuous models for the case with known and unknown nonlinearity, respectively. Then the first type of disturbances can be estimated and rejected, and the second type can be attenuated; simultaneously, the desired dynamic performances can be guaranteed. Simulations for a flight control system are given to demonstrate the effectiveness of the results and compare the proposed results with the previous schemes. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust H∞ deconvolution filtering for uncertain singular Markovian jump systems with time‐varying delays

The problem of H_∞ deconvolution filter design for a class of singular Markovian jump systems with time‐varying delays and parameter uncertainties is considered in this paper. By constructing a more comprehensive stochastic Lyapunov‐Krasovskii functional, novel delay‐dependent conditions are established to guarantee the filtering error system is not only stochastically admissible, but also satisfies a prescribed H_∞‐norm level for all admissible uncertainties. The desired filter parameters can be obtained by solving a set of strict linear matrix inequalities. Two examples and an electrical RLC circuit example are employed to verify the effectiveness and usefulness of the proposed methods in the paper. Copyright © 2015 John Wiley & Sons, Ltd.     

New approach to H ∞ filtering of two‐dimensional T‐S fuzzy systems

This paper is concerned with the H _∞ filtering problem for two‐dimensional T‐S fuzzy systems. Sufficient conditions for the solvability of this problem are obtained by using basis‐dependent Lyapunov functions. By considering the measured output as an independent variable with respect to the state variable and the disturbance input, a new method for designing two‐dimensional H _∞ filters is presented. Moreover, it has been shown that the proposed method is equivalent to the conventional one. Therefore, the proposed method does not lead to any conservativeness that may be caused by separately considering the measured output, the state variable, and the disturbance input. In converting the parameterized linear matrix inequalities (PLMI) into LMI constraints, attention is focused on the reduction of the number of LMI‐based conditions. On the basis of the proposed theorem, the number of LMI‐based conditions is reduced to r³ from r³(r + 1)² ∕ 4 by the conventional method. Thus, the computational advantage is obvious for fuzzy systems with large number of fuzzy rules. Simulation results have demonstrated the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

一类不确定非线性离散时滞系统的鲁棒H∞滤波设计

考虑一类同时带有非线性动态和参数不确定性的离散时滞系统的鲁棒H-infinity滤波设计问题. 假设参数不确定性具有线性分式形式, 而非线性动态满足Lipschitz条件, 给出滤波器使误差系统鲁棒渐近稳定且达到指定的干扰抑制水平. 对参数已知情形, 先建立广义有界实引理, 然后给出H-infinity滤波器的存在条件, 证明了H-infinity滤波器的存在性可归结为线性矩阵不等式的可解性, 基于线性矩阵不等式给出了H-infinity滤波器的综合方法和步骤. 对参数不确定性情形, 通过引进标度参数, 将不确定非线性离散时滞系统的鲁棒H-infinity滤波问题转化为确定系统的H-infinity滤波设计. 最后给出仿真例子验证所得结果的有效性.     

一类不确定非线性离散时滞系统的鲁棒H∞滤波设计

考虑一类同时带有非线性动态和参数不确定性的离散时滞系统的鲁棒H∞滤波设计问题．假设参数不确定性具有线性分式形式,而非线性动态满足Lipschitz条件,给出滤波器使误差系统鲁棒渐近稳定且达到指定的干扰抑制水平．对参数已知情形,先建立广义有界实引理,然后给出H∞滤波器的存在条件,证明了H∞滤波器的存在性可归结为线性矩阵不等式的可解性,基于线性矩阵不等式给出了H∞滤波器的综合方法和步骤．对参数不确定性情形,通过引进标度参数,将不确定非线性离散时滞系统的鲁棒H∞滤波问题转化为确定系统的H∞滤波设计．最后给出仿真例子验证所得结果的有效性．     

On-line frequency-and time-domain identification of a linear multivariable system

A method for the on-line identification of a linear multivariable plant subject to both deterministic and stochastic disturbances is proposed. The identification scheme rests on the use of a sum of sinusoids of distinct frequencies as probing-signal inputs and on the employment of linear time-varying filters to filter the plant inputs and the plant outputs. The time-varying filters are essentially banks of narrow-band filters tuned to the probing-signal frequencies. The filtered plant inputs and the filtered plant outputs yield an estimate of the plant transfer function matrix at the probing-signal frequencies. The filtered data are further processed using a recursive least-squares algorithm and a time-domain model estimate is obtained in terms of the coefficients of the difference equation relating each input-output pair. The identification algorithm is decoupled in the sense that the estimate of the transfer function or difference equation between the ith input and jth output is unaffected by other inputs or outputs. Simulation results on the performance of the time-varying filter and the identification scheme are given.     

Robust H∞ filtering for a class of Markovian jump systems with time‐varying delays based on delta operator approach

In this paper, the robust H_∞ filtering problem for a class of discrete Markovian jump systems with time‐varying delays and linear fractional uncertainties is investigated based on delta operator approach. Based on Lyapunov‐Krasovskii functional in delta domain, new delay‐dependent sufficient conditions for the solvability of this problem are presented in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired jump H_∞ filter is given. The proposed method can unify some previous related continuous and discrete systems into the delta operator systems framework. Numerical examples are given to illustrate the effectiveness of the developed techniques. © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Weighted‐average ℓ1 filtering for switched positive systems

In this paper, the filtering problem for a class of switched positive systems with dwell time is investigated. A novel weighted‐average technique is proposed for filter design such that the final estimate of the unmeasurable outputs of the considered system is more accurate than that of traditional approaches. The main contributions of this paper are summarized as follows: By exploiting the positivity and characteristics of switched positive systems with dwell time, a candidate linear copositive Lyapunov function, which is both quasi‐time‐dependent and mode‐dependent, is presented to establish the closed‐loop stability of the considered systems. Upon the established closed‐loop stability, less conservative bounded positive filters (both upper‐bound and lower‐bound filter) with ? ₁ disturbance attenuation performance are designed for the considered system. By introducing a proper weight, a weighted‐average approach, which is more general than the bounded filter design method, is proposed for filter design. The worst ? ₁ disturbance attenuation performance of the novel developed filter is evaluated. Both the bounded filters and the weighted‐average filter are designed by solving standard linear programming problems. A numerical example illustrates the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.     

Robust ℋ∞ filtering of Markovian jump stochastic systems with uncertain transition probabilities

This article investigates the problem of robust ?_∞ filtering for a class of uncertain Markovian stochastic systems. The system under consideration not only contains Itô-type stochastic disturbances and time-varying delays, but also involves uncertainties both in the system matrices and in the mode transition rate matrix. Our aim is to design an ?_∞ filter such that, for all admissible parameter uncertainties and time-delays, the filtering error system can be guaranteed to be robustly stochastically stable, and achieve a prescribed ?_∞ disturbance rejection attenuation level. By constructing a proper stochastic Lyapunov–Krasovskii functional and employing the free-weighting matrix technique, sufficient conditions for the existence of the desired filters are established in terms of linear matrix inequalities, which can be readily solved by standard numerical software. Finally, a numerical example is provided to show the utility of the developed approaches.     

Robust output feedback control against disturbance filter uncertainty described by dynamic integral quadratic constraints

Motivated by a robust disturbance rejection problem, in which disturbances are described by an uncertain filter at the plant input, a convex solution is presented for the robust output feedback controller synthesis problem for a particularly structured plant. The uncertainties are characterized by an integral quadratic constraint (IQC) with general frequency‐dependent multipliers. By exploiting the structure of the generalized plant, linear matrix inequality (LMI)‐synthesis conditions are derived in order to guarantee a specified ??₂‐gain or ??₂‐norm performance level, provided that the IQC multipliers are described by LMI constraints. Moreover, it is shown that part of the controller variables can be eliminated. Finally, the rejection of non‐stationary sinusoidal disturbance signals is considered. In a numerical example, it is shown that specifying a bound on the rate‐of‐variation of the time‐varying frequency can improve the performance if compared with the static IQC multipliers. Copyright © 2009 John Wiley & Sons, Ltd.     

Tracking Performance Achievement for Continuous‐Time Delayed Linear Systems Subject to Actuator Saturation and output Disturbances

Controlling continuous‐time input‐delayed nonminimum‐phase linear systems is addressed in the presence of actuator saturation and output‐disturbances. Focusing on output‐reference tracking, the control design is dealt with in the pseudo‐polynomials ring. A quite appealing L₂ ‐tracking performance is shown to be achievable in the presence of arbitrary inputs i.e. the output reference and the output disturbance. The performance is formulated in terms of a well defined output‐reference mismatch error (ORME), depending on the inputs’ rate and their compatibility with the actuator saturation constraint.