具有测量数据部分丢失的离散系统的H∞滤波器设计

For packet-based transmission of data over a network, or temporary sensor failure, etc., data samples may be missing in the measured signals. This paper deals with the problem of H∞ filter design for linear discrete-time systems with missing measurements. The missing measurements will happen at any sample time, and the probability of the occurrence of missing data is assumed to be known. The main purpose is to obtain both full-and reduced-order filters such that the filter error systems are exponentially mean-square stable and guarantee a prescribed H∞ performance in terms of linear matrix inequality (LMI). A numerical example is provided to demonstrate the validity of the proposed design approach.     

Robust H ∞ filter design for time-delay systems with saturation

This paper investigates the H∞ filtering problem for a class of linear continuous-time systems with both time delay and saturation. Such systems have time delay in their state equations and saturation in their output equations, and their process and measurement noises have unknown statistical characteristics and bounded energies. Based on the Lyapunov-Krasovskii stability theorem and the linear matrix inequalities (LMIs) technique, a generalized dynamic filter architecture is proposed, and a filter design method is developed. The linear H∞ filter designed by the method can guarantee the H∞ performance. The parameters of the designed filter can be obtained by solving a kind of LMI. An illustrative example shows that the design method proposed in this paper is very effective.     

考虑有限字长影响的离散时间非脆弱H∞滤波

The nonfragile H_∞filtering problem affected by finite word length (FWL) for linear discrete-time systems is investigated in this paper.The filter to be designed is assumed to be with additive gain variations,which reflect the FWL effects on filter implementation.A notion of structured vertex separator is proposed to deal with the problem and exploited to develop sufficient conditions for the nonfragile H_∞filter design in terms of a set of linear matrix inequalities (LMIs).The design renders the augmented system asymptotically stable and guarantees the H_∞attenuation level less than a prescribed level.A numerical example is given to illustrate the effect of the proposed method.     

Robust H-infinity filtering for time-delay systems with missing measurements： a parameter-dependent approach

Robust H-infinity filtering for a class of uncertain discrete-time linear systems with time delays and missing measurements is studied in this paper. The uncertain parameters are supposed to reside in a convex polytope and the missing measurements are described by a binary switching sequence satisfying a Bernoulli distribution. Our attention is focused on the analysis and design of robust H-infinity filters such that, for all admissible parameter uncertainties and all possible missing measurements, the filtering error system is exponentially mean-square stable with a prescribed H-infinity disturbance attenuation level. A parameter-dependent approach is proposed to derive a less conservative result. Sufficient conditions are established for the existence of the desired filter in terms of certain linear matrix inequalities （LMIs）. When these LMIs are feasible, an explicit expression of the desired filter is also provided. Finally, a numerical example is presented to illustrate the effectiveness and applicability of the proposed method.     

Mixed <Emphasis Type="Italic">H</Emphasis><Subscript>2</Subscript>/<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> filtering for a class of high-speed sampling uncertain systems

The problem of mixed H2/H∞ filtering for polytopic Delta operator systems is investigated. The aim is to design a linear asymptotically stable filter which guarantees that the filtering error system has different performances in different filtering channels. Based on a parameter-dependent Lyapunov function, a new mixed H2/H∞ performance criterion is presented. Upon this performance criterion, a sufficient condition for the full-order mixed H2/H∞ filter is derived in terms of linear matrix inequalities. The filter can be obtained from the solution of a convex optimization problem. The proposed filter design procedure is less conservative than the strategy based on the quadratic stability notion. A numerical example is given to illustrate the feasibility 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.     

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 t...     

Robust H_∞ control for discrete-time polytopic uncertain systems with linear fractional vertices

The robust H∞ control problem for discrete-time uncertain systems is investigated in this paper. The uncertain systems are modelled as a polytopic type with linear fractional uncertainty in the vertices. A new linear matrix inequality (LMI) characterization of the H∞ performance for discrete systems is given by introducing a matrix slack variable which decouples the matrix of a Lyapunov function candidate and the parametric matrices of the system. This feature enables one to derive sufficient conditions for discrete uncertain systems by using parameter-dependent Lyapunov functions with less conservativeness. Based on the result, H∞ performance analysis and controller design are carried out. A numerical example is included to demonstrate the effectiveness of the proposed results.     

Robust H_∞ Filtering for a Class of Uncertain Lurie Time-delay Singular Systems

This paper deals with the problem of the robust H∞filtering for a class of Lurie singular systems with state time-delays, parameter uncertainties and unknown statistics characteristics but with limited power disturbance,aiming to design a robustly stable filter such that the uncertain Lurie time-delay singular systems are not only regular,impulse free and stable,but also have a prescribed level of H∞performance for the filtering error dynamics for all admissible uncertainties．A sufficient condition for the existence of such a filter is proposed in terms of linear matrix inequalities (LMIs)．When a solution to this set of LMIs exists,the parametric matrices of a desired filter can be easily obtained using LMI toolbox．     

Mixed H_2/H_∞ filtering for a class of high-speed sampling uncertain systems

The problem of mixed H_2/H_∞ filtering for polytopic Delta operator systems is investigated. The aim is to design a linear asymptotically stable filter which guarantees that the filtering error system has different performances in different filtering channels. Based on a parameter-dependent Lyapunov function, a new mixed H_2/H_∞ performance criterion is presented. Upon this performance criterion, a sufficient condition for the full-order mixed H_2/H_∞ filter is derived in terms of linear matrix inequalities. The filter can be obtained from the solution of a convex optimization problem. The proposed filter design procedure is less conservative than the strategy based on the quadratic stability notion. A numerical example is given to illustrate the feasibility of the proposed approach.     

Reliable H-infinity filtering for linear systems with sensor saturation

In this paper, a new reliable H-infinity filter design problem is proposed for a class of continuous-time systems with sensor saturation and failures. Attention is focused on the analysis and synthesis problems of a full order reliable H-infinity filter such that the filtering error dynamics is asymptotically stable with a guaranteed disturbance rejection attenuation level γ. It is shown that the filtering error dynamics obtained from the original system plus the filter can be modeled by a linear system with sector bounded nonlinearity. The design conditions are given in terms of solutions to a set of linear matrix inequalities (LMIs). These conditions are then considered in a convex optimization problem with LMIs constraints in order to design an optimal reliable H-infinity filter. A numerical example is given to illustrate the effectiveness of the proposed results.     

Fuzzy H_∞ Filter Design for a Class of Nonlinear Systems with Time Delays via LMI

This paper develops fuzzy H_∞filter for state estimation approach for nonlinear discrete- time systems with multiple time delays and unknown bounded disturbances.We design a stable fuzzy H_∞filter based on the Takagi-Sugeno (T-S) fuzzy model,which assures asymptotic stability and a prescribed H_∞index for the filtering error system.Sufficient condition for the existence of such a filter is established by solving the linear matrix inequality (LMI) problem.The LMI problem can be efficiently solved with global convergence using the interior point algorithm.Simulation examples are provided to illustrate the design procedure of the proposed method.     

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 suficient 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 effciently 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.     

一类离散非线性不确定时滞系统的鲁棒滑模滤波

This paper is concerned with the problem of robust sliding-mode filtering for a class of uncertain nonlinear discrete-time systems with time-delays. The nonlinearities are assumed to satisfy global Lipschitz conditions and parameter uncertainties are supposed to reside in a polytope. The resulting filter is of the Luenberger type with the discontinuous form. A sufficient condition with delay-dependency is proposed for existence of such a filter. And the desired filter can be found by solving a set of matrix inequalities. The resulting filter adapts for the systems whose noise input is real functional bounded and not be required to be energy bounded. A numerical example is given to illustrate the effectiveness of the proposed design method.     

Delay-dependent Non-fragile H∞ Filtering for Uncertain Fuzzy Systems Based on a 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.     

Delay-dependent robust stabilization and H ∞ control for uncertain stochastic T-S fuzzy systems with discrete interval and distributed time-varying delays

In this paper, delay-dependent robust stabilization and H∞ control for uncertain stochastic Takagi-Sugeno (T-S) fuzzy systems with discrete interval and distributed time-varying delays are discussed. The purpose of the robust stochastic stabilization problem is to design a memoryless state feedback controller such that the closed-loop system is mean-square asymptotically stable for all admissible uncertainties. In the robust H∞ control problem, in addition to the mean-square asymptotic stability requirement, a prescribed H∞ performance is required to be achieved. Sufficient conditions for the solvability of these problems are proposed in terms of a set of linear matrix inequalities (LMIs) and solving these LMIs, a desired controller can be obtained. Finally, two numerical examples are given to illustrate the effectiveness and less conservativeness of our results over the existing ones.     

Robust fault detection filter design for a class of time-delay systems via equivalent transformation

This paper is concerned with the robust fault detection filter (RFDF) design for a class of linear timeinvariant systems (LTISs) with output state time delays. Although existing results in literatures study the RFDF for timedelay systems, few is concerned with the output state time-delay systems. The basic idea of our study is to eliminate the time delays of system and transform it to a delay-free system (i.e., a linear time-invariant system without time delays) by the bicausal change of coordinates approach. Then, we design the RFDF for the delay-free LTIS, which is equivalent to the original system with time delays. We first introduce a class of systems with output state time delays, whose fault can be detected by using the RFDF design approach for delay-free systems. Then, since the RFDF design problem can be formulated as a standard H-infinity-model matching problem, it is solved by using H-infinity-optimization LMI techniques. In the last, the adaptive threshold of fault detection is chosen and an illustrative design example is used to demonstrate the validity of the design approach.     

Fault detection for a class of impulsive switched systems

The problem of fault detection for a class of nonlinear impulsive switched systems is investigated in this paper. Fault detection filters are designed such that the augmented systems are stable, and the residual error signal generated by the filters guarantees the H∞ performance for disturbances and faults. Sufficient conditions for the design of fault detection(FD) filters are presented by linear matrix inequalities. Moreover, the filter gains are characterized according to a solution of a convex optimization. Finally, an example derived from a pulse-width-modulation-driven boost converter is given to illustrate the effectiveness of the FD design approach.     

非线性摄动系统的鲁棒故障诊断滤波器设计ILMI算法

The robust fault detection filter design for uncertain linear systems with nonlinear perturbations is formulated as a two-objective optimization problem. Solvable conditions for the exis- tence of such a robust fault detection filter are given in terms of matrix inequalities (MIs), which can be solved by applying iterative linear matrix inequality (ILMI) techniques. Particularly, compared with two existing LMI methods, the developed algorithm is more generalized and less conservative. An illustrative example is given to show the effectiveness of the proposed method.     

Robust Dissipative Control for Linear Multi-variable Systems

Robust quadratic dissipative control for a class of linear multi-variable systems with pa- rameter uncertainties is considered,where the uncertainties are expressed in a linear fractional form. For the nominal system without uncertainties,the equivalence between quadratic dissipativeness and positive realness is established,and conditions are derived for linear systems to be quadratic dissi- pative.As for uncertain systems,it is shown that the robust quadratic dissipative control problem for the uncertain system can be reduced to the corresponding problem for a related system without uncertainties.The control problem concerned can be solved using LMI approach.The results of the paper unify existing results on H_∞control and positive real control and provide a more flexible and less conservative control design method.