Observer-based H∞ controller for 2-D T–S fuzzy model

This paper develops a method of fuzzy observer-based H_∞ controller design for two-dimensional (2-D) discrete Takagi–Sugeno (T–S) fuzzy systems. By reformulating the system, a linear matrix inequality (LMI)-based sufficient condition is derived. Then the fuzzy controller and the fuzzy observer can be independently designed, which guarantee an H_∞ noise attenuation γ of the whole system. Owing to the introduction of free matrices, the presented design method has a wider range of application and can guarantee a better H_∞ performance of the closed-loop fuzzy control system. Simulation results have demonstrated the effectiveness of the proposed method.     

H ∞ control for 2-D singular delayed systems

This article considers the problem of H _∞ control for two-dimensional (2-D) singular delayed systems in Roesser models. The problem to be addressed is the design of a state feedback controller such that the acceptability, internal stability and causality of the resulting closed-loop system is guaranteed and a prescribed H _∞ performance level is ensured. In terms of a linear matrix inequality (LMI), a sufficient condition for the solvability of the problem is obtained. A desired state feedback controller can be designed by solving a certain LMI. A numerical example is provided to demonstrate the application of the proposed method.     

An iterative approach to H−/H∞ Fault Detection Observer Design for Discrete‐Time Uncertain Systems

In this paper, H _?/H _∞ multi‐objective fault detection observer design problem for linear discrete‐time systems is studied. Owing to the model inaccuracy in practical situations, system uncertainty is considered as well as the structure of the uncertainty. Sufficient conditions for the existence of the observers to guarantee the fault sensitivity and disturbance robustness in infinite frequency domain are presented. A new iterative linear matrix inequality (LMI) algorithm for the observers are proposed to obtain the solutions. In order to reduce the conservativeness, the observer design problem in finite frequency domain is also investigated. Simulation results illustrate the effectiveness of the proposed methods.     

An LMI approach to design robust fault detection filter for uncertain LTI systems

In this paper, the robust fault detection filter design problem for uncertain linear time-invariant (LTI) systems with both unknown inputs and modelling errors is studied. The basic idea of our study is to use an optimal residual generator (assuming no modelling errors) as the reference residual model of the robust fault detection filter design for uncertain LTI systems with modelling errors and, based on it, to formulate the robust fault detection filter design as an H_∞ model-matching problem. By using some recent results of H_∞ optimization, a solution of the optimization problem is then presented via a linear matrix inequality (LMI) formulation. The main results include the development of an optimal reference residual model, the formulation of robust fault detection filter design problem, the derivation of a sufficient condition for the existence of a robust fault detection filter and a construction of it based on the LMI solution parameters, the determination of adaptive threshold for fault detection. An illustrative design example is employed to demonstrate the effectiveness of the proposed approach.     

Design and analysis of robust fault detection filter using LMI tools

In this paper, the robust fault detection filter design problem for linear time invariant (LTI) systems with unknown inputs and modeling uncertainties is studied. The basic idea of our study is to formulate the robust fault detection filter design as a H_∞ model-matching problem. A solution of the optimal problem is then presented via a linear matrix inequality (LMI) formulation. The main results include the formulation of robust fault detection filter design problems, the derivation of a sufficient condition for the existence of a robust fault detection filter and construction of a robust fault detection filter based on the iterative of LMI algorithm.     

Sensor fault estimation for Lipschitz nonlinear systems in finite-frequency domain

In this study, the problem of sensor fault estimation observer design for Lipschitz nonlinear systems with finite-frequency specifications is investigated. First, the sensor fault is considered as an auxiliary state vector and an augmented system is established. Then, by transforming the nonlinear error dynamics into a linear parameter varying system, a sufficient condition for the observer-error system with a finite-frequency H_∞ performance is derived in terms of linear matrix inequalities (LMIs). Based on the obtained condition, novel nonlinear observers are designed to simultaneously estimate the system states and the fault signals and attenuate the disturbances in the finite-frequency domain. The proposed design method can provide less restrictive LMI conditions and get a better disturbance-attenuation performance when the frequency ranges of disturbances are known beforehand. A numerical example is given to show the effectiveness and superiority of the new results.     

Fault detection for discrete piecewise linear systems with infinite distributed time-delays

In this paper, the fault detection problem is investigated for a class of discrete-time piecewise linear systems with external disturbances and infinite distributed time-delays. As a modelling framework, piecewise linear system often arise when piecewise linear components are encountered, such as dead-zone, saturation, relays and hysteresis. The time-delays are assumed to be infinitely distributed in the discrete-time domain. The aim of this paper is to detect the possible faults and to estimate the system state. For this purpose, firstly, stability analysis is given based on a piecewise smooth Lyapunov function. Afterward, an appropriate approach of fault detection and filter design problem is provided to achieve a satisfactory balance between the disturbances attenuation level γ and the sensitivity to the fault for piecewise linear systems. As a consequence, a sufficient condition is obtained in terms of the linear matrix inequalities such that, for all admissible infinite distributed time-delays and external disturbances, the system is guaranteed to be asymptotically stable and the residual is guaranteed to satisfy H_∞ filtering performance and fault detection performance. At last, a simulation example is provided to demonstrate the applicability and effectiveness of the fault detection filtering scheme proposed in this paper.     

Robust H ∞ reliable control of time delay nonlinear systems via Takagi–Sugeno fuzzy models

This article is focused on reliable fuzzy H _∞ controller design for a class of Takagi–Sugeno (T–S) fuzzy systems with state delay, actuator failures, disturbance input and norm bounded uncertainties. In the design, the H _∞ performance of the closed-loop system is optimised during normal operation (without failures) while the system satisfies a prescribed H _∞ performance level in the case of actuator failures. Two methods are presented in this study. In the first method, delay-dependent conditions are derived based on a single Lyapunov–Krasovskii function. This method improves delay-independent results existing in the literature. Next, to further reduce the conservatism, we use a parameter-dependent Lyapunov–Krasovskii function. The new sufficient conditions for the existence of the suboptimal robust reliable controller are shown in terms of linear matrix inequalities (LMIs), which can be solved by using LMI optimisation techniques. A simulation example shows the effectiveness of the proposed methods.     

H ∞ filtering for discrete-time singular networked systems with communication delays and data missing

In this article, the problem of H _∞ filter design is investigated for discrete-time singular networked systems with both multiple stochastic time-varying communication delays and probabilistic missing measurements. Two kinds of stochastic time-varying communication delays, namely stochastic discrete delays and stochastic distributed delays, are simultaneously considered. The purpose of the addressed filtering problem is to design a filter such that, for the admissible random measurement missing and communication delays, the filtering error dynamics is asymptotically stable in the mean square with a prescribed H _∞ performance index. In terms of linear matrix inequality (LMI) method, a sufficient condition is established that ensures the asymptotical stability in the mean square with a prescribed H _∞ performance index of the filtering error dynamics and then the filter parameters are characterised by the solution to an LMI. A numerical example is introduced to demonstrate the effectiveness of the proposed design procedures.     

A single dynamic observer-based module for design of simultaneous fault detection,isolation and tracking control scheme

The problem of simultaneous fault detection, isolation and tracking (SFDIT) control design for linear systems subject to both bounded energy and bounded peak disturbances is considered in this work. A dynamic observer is proposed and implemented by using the H_∞/H_?/L₁ formulation of the SFDIT problem. A single dynamic observer module is designed that generates the residuals as well as the control signals. The objective of the SFDIT module is to ensure that simultaneously the effects of disturbances and control signals on the residual signals are minimised (in order to accomplish the fault detection goal) subject to the constraint that the transfer matrix from the faults to the residuals is equal to a pre-assigned diagonal transfer matrix (in order to accomplish the fault isolation goal), while the effects of disturbances, reference inputs and faults on the specified control outputs are minimised (in order to accomplish the fault-tolerant and tracking control goals). A set of linear matrix inequality (LMI) feasibility conditions are derived to ensure solvability of the problem. In order to illustrate and demonstrate the effectiveness of our proposed design methodology, the developed and proposed schemes are applied to an autonomous unmanned underwater vehicle (AUV).     

Anti-disturbance control for time-varying delay Markovian jump nonlinear systems with multiple disturbances

In this paper, the problem of composite anti-disturbance resilient control is addressed for time-varying delay Markovian jump nonlinear systems with multiple disturbances. The disturbances are assumed to include two parts: the first one in the input channel is described by an external system with perturbations; the second one is supposed to be bounded H₂ norm. By combining disturbance observer and L₂–L_∞ control method, the disturbances are attenuated and rejected, simultaneously, and the desired dynamic performance can be obtained for time-varying delay Markovian jump nonlinear systems. Moreover, the gains of the resilient controller and the observer are acquired by applying linear matrix inequalities (LMIs) technology. Finally, an application example is presented to show the effectiveness of the proposed approach.     

Robust H ∞ filter design of uncertain T-S fuzzy neutral systems with time-varying delays

This article addresses the problem of robust H _∞ filter design of a class of Takagi–Sugeno fuzzy neutral systems with time-varying delays and norm-bounded parameter uncertainties. A fuzzy filter is constructed, which ensures both the robust stability and a prescribed H _∞ performance of the filtering error system. A linear matrix inequality approach is developed, and a delay-dependent sufficient condition is obtained. A simulation example is provided to demonstrate the effectiveness of the proposed approach.     

Robust output-feedback control of linear discrete-time systems

The problem of designing H_∞ dynamic output-feedback controllers for linear discrete-time systems with polytopic type parameter uncertainties is considered. Given a transfer function matrix of a system with uncertain real parameters that reside in some known ranges, an appropriate, not necessarily minimal, state-space model of the system is described which permits reconstruction of all its states via the delayed inputs and outputs of the plant. The resulting model incorporates the uncertain parameters of the transfer function matrix in the state-space matrices. A recently developed linear parameter-dependent LMI approach to state-feedback H_∞ control of uncertain polytopic systems is then used to design a robust output-feedback controllers that are of order comparable to the one of the plant. These controllers ensure the stability and guarantee a prescribed performance level within the uncertainty polytope.     

State-feedback ℋ∞ control for stochastic time-delay nonlinear systems with state and disturbance-dependent noise

This article focuses on the state-feedback ?_∞ control problem for the stochastic nonlinear systems with state and disturbance-dependent noise and time-varying state delays. Based on the maxmin optimisation approach, both the delay-independent and the delay-dependent Hamilton–Jacobi-inequalities (HJIs) are developed for synthesising the state-feedback ?_∞ controller for a general type of stochastic nonlinear systems. It is shown that the resulting control system achieves stochastic stability in probability and the prescribed disturbance attenuation level. For a class of stochastic affine nonlinear systems, the delay-independent as well as delay-dependent matrix-valued inequalities are proposed; the resulting control system satisfies global asymptotic stability in the mean-square sense and the required disturbance attenuation level. By modelling the nonlinearities as uncertainties in corresponding stochastic time-delay systems, the sufficient conditions in terms of a linear matrix inequality (LMI) and a bilinear matrix inequality (BMI) are derived to facilitate the design of the state-feedback ?_∞ controller. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.     

Synthesis of stochastic fault tolerant control systems with random FDI delay

In this work, the synthesis of fault tolerant control (FTC) for stochastic stability and H _∞ performance is studied. Occurrence of faults in the system is governed by a Markov Chain, so the open-loop system is modelled as a linear system with Markovian jumping parameters. The fault detection and isolation (FDI) decision is modelled as another random process that will indicate the fault mode after an exponentially distributed random delay. This stochastic formulation of FTC concerns the random nature of faults and the effect of random fault detection delay on the overall system, and can be regarded as an extension to the traditional reconfigurable control problem. In this paper, output feedback controllers are designed using an iterative LMI algorithm for mean exponential stability (MES) and the H _∞ performance. Model uncertainties and external disturbance are also considered in the robust design.     

Fault detection of discrete-time switched systems with distributed delays: input–output approach

This article is concerned with the ?_∞ fault detection of discrete-time switched systems with distributed delays. By using the input–output approach combining with the small-scale gain theorem, a sufficient condition is established in terms of linear matrix inequality, which guarantees the fault detection system to be exponentially stable with an ?_∞ performance. Then, a solvability condition for the desired fault detection filter is also proposed. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed theory.     

Integrated fault estimation and fault‐tolerant control for uncertain Lipschitz nonlinear systems

This paper proposes an integrated fault estimation and fault‐tolerant control (FTC) design for Lipschitz non‐linear systems subject to uncertainty, disturbance, and actuator/sensor faults. A non‐linear unknown input observer without rank requirement is developed to estimate the system state and fault simultaneously, and based on these estimates an adaptive sliding mode FTC system is constructed. The observer and controller gains are obtained together via H_∞ optimization with a single‐step linear matrix inequality (LMI) formulation so as to achieve overall optimal FTC system design. A single‐link manipulator example is given to illustrate the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Asynchronous fault detection observer design for discrete‐time piecewise linear systems

This paper studies the problem of asynchronous fault detection (FD) observer design for piecewise linear systems. Considering that the states of the FD observer and the system may stay at different regions of the state space, asynchronous FD observers are designed at different instants to cope with the challenges incurred by exogenous disturbances and fault signals. By employing new piecewise Lyapunov functions that depend on the different regions where the states are located, it is proved that the proposed asynchronous FD observers ensure the stability and H_∞ performance of the error systems. Three examples are given to show that the new design scheme provides better FD results than the existing design methods.