New reduced-order <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> filter design method for discrete-time singular systems with lossy measurements by strict LMI approach

In this paper, the new design problems of full and reduced-order H _∞ filters including static filters are investigated for discrete-time singular systems with lossy measurements. The lossy measurement is described by a stochastic variable satisfying Bernoulli random binary distribution to model the measured output. Being different from the previous results, the filter existence condition by a new Lyapunov function for singular systems with lossy measurements is given using a strict linear matrix inequality (LMI) in terms of all variables. The proposed full and reduced-order H _∞ filter guarantees regularity, causality, and mean-square stochastic stability with a H _∞ performance bound of filtering error singular system. Moreover, it is shown that the reduced-order H _∞ filter design method is general for both singular systems and non-singular systems with lossy measurements. Numerical examples are worked out to illustrate the effectiveness and applicability of the proposed method.     

Reduced-order filtering for networks with Markovian jumping parameters and missing measurements

The problem of reduced-order H _∞ filters design for Markovian jumping complex networks with polytopic time-varying transition probability matrices is first addressed in this paper, where the dynamic of each node is described by the sector-bounded nonlinearity. For the measurements, both quantisation and packet dropouts are considered, where each node has its own packet dropout rate. By using the mode- and transition probability-dependent Lyapunov function approach, two sufficient conditions are provided to ensure the stochastic stability and the disturbance attenuation performance of the resulting filtering error system. Then, the mode-independent reduced-order filters design method is proposed, and the filter parameters are given explicitly by linear matrix inequality method. Finally, the effectiveness of the theoretic results presented is illustrated via a numerical example which contains performance comparison of different mode-independent reduced-order filters.     

H∞ filter design for a class of nonlinear discrete-time singular systems

This paper deals with the H_∞ filter design problem for a class of discrete-time Lipschitz nonlinear singular systems. The approach is based on the parameterisation of the obtained algebraic constraints from the estimation errors. Sufficient conditions for the existence of the filters which guarantee stability and the worst case filter error energy over all bounded energy disturbances is minimised are given. The method also unifies the design for the full-order, reduced-order, minimal-order filters for discrete- time systems. The presented results are less conservative than those existing in the literature, this is due to the introduction of new slack variables. Application to systems with unknown input is presented via a numerical example.     

随机时延网络化不确定系统的鲁棒H∞滤波

研究了一类具有随机时延的网络化不确定系统的 H∞ 滤波器设计问题. 这类时延的产生是由于传感器和滤波器通过有限带宽的网络连接而引起的系统测量数据的滞后, 而且它是随机发生的. 本文采用满足 Bernoulli 分布随机变量来描述测量数据的这种随机时延. 利用线性矩阵不等式, 给出了全阶和降阶的滤波器存在的充分条件. 所设计的滤波器使得滤波误差系统是均方指数稳定且具有给定的H∞ 性能. 数值仿真表明设计方法的有效性.     

Reduced-order ℓ2-ℓ∞ filtering for discrete-time T-S fuzzy systems with stochastic perturbation

This paper is concerned with the problem of ?₂-?_∞ filtering for discrete-time Takagi-Sugeno (T-S) fuzzy systems with stochastic perturbation. Firstly, a basis-dependent existence condition of desirable ?₂-?_∞ filters is proposed. Then by means of the convex linearisation technique, the derived condition is transformed into some strict linear matrix inequality (LMI) constraints, by which both full- and reduced-order filters can be designed. Moreover, for the reduced-order ?₂-?_∞ filter design, a novel analysis and design method with the projection lemma is also provided. Finally, a numerical example is provided to illustrate the feasibility and effectiveness of the proposed full- and reduced-order ?₂-?_∞ filter design methods.     

New results on robust H ∞ filtering design for discrete-time piecewise linear delay systems

This paper revisits the problem of robust H _∞ filtering design for a class of discrete-time piecewise linear state-delayed systems. The state delay is assumed to be time-varying and of an interval-like type, which means that both the lower and upper bounds of the time-varying delay are available. The parameter uncertainties are assumed to have a structured linear fractional form. Based on a novel delay-dependent piecewise Lyapunov–Krasovskii functional combined with Finsler's Lemma, a new delay-dependent sufficient condition for robust H _∞ performance analysis is first derived and then the filter synthesis is developed. It is shown that by using a new linearisation technique, a unified framework can be developed so that both the full-order and reduced-order filters can be obtained by solving a set of linear matrix inequalities (LMIs), which are numerically efficient with commercially available software. Finally, a numerical example is provided to illustrate the effectiveness and less conservatism of the proposed approach.     

Robust H ∞ filtering for networked systems with multiple state delays

In this paper, a new robust H _∞ filter design problem is studied for a class of networked systems with multiple state-delays. Two kinds of incomplete measurements, namely, measurements with random delays and measurements with stochastic missing phenomenon, are simultaneously considered. Such incomplete measurements are induced by the limited bandwidth of communication networks, and are modelled as a linear function of a certain set of indicator functions that depend on the same stochastic variable. Attention is focused on the analysis and design problems of a full-order robust H _∞ filter such that, for all admissible parameter uncertainties and all possible incomplete measurements, the filtering error dynamics is exponentially mean-square stable and a prescribed H _∞ attenuation level is guaranteed. Some recently reported methodologies, such as delay-dependent and parameter-dependent stability analysis approaches, are employed to obtain less conservative results. Sufficient conditions, which are dependent on the occurrence probability of both the random sensor delay and missing measurement, are established for the existence of the desired filters in terms of certain linear matrix inequalities (LMIs). When these LMIs are feasible, the explicit expression of the desired filter can also be characterized. Finally, numerical examples are given to illustrate the effectiveness and applicability of the proposed design method.     

H ∞ filtering for stochastic systems with time-varying delay

This article considers the problem of H _∞ filter design for stochastic systems with time-varying delay. The time delay is assumed to be of interval type. Attention is focused on the design of delay-dependent filters that guarantee the asymptotic stability in mean square and a prescribed noise attenuation level in an H _∞ sense for the filtering error dynamics. The delay-dependent H _∞ filter design scheme is proposed in terms of a linear matrix inequality. A numerical example is used to illustrate the effectiveness of the proposed approach.     

Reduced-order filtering for singular systems

This paper solves the problem of reduced-order H_∞ filtering for singular systems. The purpose is to design linear filters with a specified order lower than the given system such that the filtering error dynamic system is regular, impulse-free (or causal), stable, and satisfies a prescribed H_∞ performance level. One major contribution of the present work is that necessary and sufficient conditions for the solvability of this problem are obtained for both continuous and discrete singular systems. These conditions are characterized in terms of linear matrix inequalities (LMIs) and a coupling non-convex rank constraint. Moreover, an explicit parametrization of all desired reduced-order filters is presented when these inequalities are feasible. In particular, when a static or zeroth-order H_∞ filter is desired, it is shown that the H_∞ filtering problem reduces to a convex LMI problem. All these results are expressed in terms of the original system matrices without decomposition, which makes the design procedure simple and directly. Last but not least, the results have generalized previous works on H_∞ filtering for state-space systems. An illustrative example is given to demonstrate the effectiveness of the proposed approach.     

Event-triggered fuzzy filtering in networked control system for a class of non-linear system with time delays

This paper focuses on the design of H _∞ filter and event-triggered scheme for a class of continuous non-linear networked control systems (NCSs) based on fuzzy system appeared with time delays. First, we consider the discrete event-triggered (ET) scheme to make efficient utilisation of bandwidth. Under this ET-scheme, sensor releases the data only when our sampled-data plant violates the specific event-triggered condition. Second, the T-S fuzzy system is used to model the non-linear NCSs. Another purpose of this paper is to design filters involving delays. Such filters have a more general form than the delay-free filters that have been mostly considered in the traditional studies. By using the time-delay system, co-design of event-triggered scheme and H _∞ filter for the delayed NCSs is presented in a unified frame work. To choose the latest data packet and discard the dis-ordered packet logic, zero-order hold is inserted between the fuzzy filter and event generator. Then, by using the novel fuzzy Lyapunov–Krasovskii function approach with free-weighting matrix technique, H _∞ filter design of event-triggered delay NCSs is proposed. Finally, to show the effective result of our co-design method, a tunnel-diode example is given.     

Residual mode filters and H ∞ control for a class of infinite-dimensional discrete-time systems

An H _∞, control problem with measurement feedback.for infinite-dimensional discrete-time (IDDT) systems whose homogeneous parts are described by Riesz-spectra operators is considered. The aim is to construct a finite-dimensional stabilizing controller for the IDDT system that makes the H _∞ norm of the closed-loop transfer function less than a given positive number δ. For that purpose, we first formulate the IDDT system as an IDDT system in l² and derive a finite-dimensional reduced-order system for the IDDT system in l². A stabilizing controller that makes the H _∞ norm of the closed-loop transfer function less than another positive number is then constructed for the reduced-order model. The finite-dimensional controller together with a residual mode Jilter plays a role of a finite-dimensional stabilizing controller that makes the H _∞ norm of the closed-loop transfer function less than δ for the original IDDT system, if the order of the residual mode filter is chosen suficiently large.     

Reduced-order filtering design for non-linear systems with H ∞ setting

In this article, sufficient conditions are presented for the existence of an H ^∞ filter with a state dimension less than the plant. The conditions are characterised in terms of the solution to a Hamilton–Jacobi inequality, which is exactly the one used in the construction of the full-order H ^∞ filters. When these conditions hold, state-space formulae are also given for such reduced-order filters. Both affine and general non-affine non-linear systems are examined. The development uses only elementary concepts of dissipativity and differential game, thus the given proofs are simple and clear. To illustrate our result, some numerical examples are also included.     

Robust H∞ filtering for 2D continuous systems with finite frequency specifications

This paper investigates the design problem of robust H_∞ filtering for uncertain two-dimensional (2D) continuous systems described by Roesser model with polytopic uncertainties and frequency domain specifications. Our aim is to design a new filter guaranteeing an H_∞ performance level in specific finite frequency (FF) domains. Using the well-known generalised Kalman Yakubovich Popov lemma and homogeneous polynomially parameter-dependent matrices of arbitrary degrees, sufficient conditions for the existence of H_∞ filters for different FF ranges are proposed and then unified in terms of solving a set of linear matrix inequalities. Illustrative examples are provided to show the usefulness and potential of the proposed results.     

Sampled-data H∞ filtering for Markovian jump singularly perturbed systems with time-varying delay and missing measurements

In this paper, sampled-data H_∞ filtering problem is considered for Markovian jump singularly perturbed systems with time-varying delay and missing measurements. The sampled-data system is represented by a time-delay system, and the missing measurement phenomenon is described by an independent Bernoulli random process. By constructing an ?-dependent stochastic Lyapunov–Krasovskii functional, delay-dependent sufficient conditions are derived such that the filter error system satisfies the prescribed H_∞ performance for all possible missing measurements. Then, an H_∞ filter design method is proposed in terms of linear matrix inequalities. Finally, numerical examples are given to illustrate the feasibility and advantages of the obtained results.     

Adaptive robust H ∞ filter design for linear systems with time-varying uncertainty

This article studies the problem of designing robust H _∞ filters for linear uncertain systems. The uncertainty parameters are assumed to be time-varying, unknown, but bounded, which appear affinely in the matrices of system models. An adaptive mechanism is introduced to construct novel filters with variable gains, which can reduce the conservativeness of the traditional robust H _∞ filters. The proposed adaptive filter design conditions are given in terms of linear matrix inequalities. A numerical example is presented to illustrate the effectiveness of the proposed strategy.     

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.     

H∞ model reduction for negative imaginary systems

This paper is concerned with the H_∞ model reduction for negative imaginary (NI) systems. For a given linear time-invariant system that is stable and NI, our goal is to find a stable reduced-order NI system satisfying a pre-specified H_∞ approximation error bound. Sufficient conditions in terms of matrix inequalities are derived for the existence and construction of an H_∞ reduced-order NI system. Iterative algorithms are provided to solve the matrix inequalities and to minimise the H_∞ approximation error. Finally, a numerical example is used to demonstrate the effectiveness of the proposed model reduction method.     

Robust filtering for a class of discrete-time uncertain nonlinear systems: An H∞ approach

This paper deals with the H_∞ filtering problem for a class of discrete-time nonlinear systems with or without real time-varying parameter uncertainty and unknown initial state. For the case when there is no parametric uncertainty in the system, we are concerned with designing a nonlinear H_∞ filter such that the induced l₂ norm of the mapping from the noise signal to the estimation error is within a specified bound. It is shown that this problem can be solved via one Riccati equation. We also consider the design of nonlinear filters which guarantee a prescribed H_∞ performance in the presence of parametric uncertainties. In this situation, a solution is obtained in terms of two Riccati equations.