Delay‐distribution‐dependent robust stability of uncertain systems with time‐varying delay

By employing the information of the probability distribution of the time delay, this paper investigates the problem of robust stability for uncertain systems with time‐varying delay satisfying some probabilistic properties. Different from the common assumptions on the time delay in the existing literatures, it is assumed in this paper that the delay is random and its probability distribution is known a priori. In terms of the probability distribution of the delay, a new type of system model with stochastic parameter matrices is proposed. Based on the new system model, sufficient conditions for the exponential mean square stability of the original system are derived by using the Lyapunov functional method and the linear matrix inequality (LMI) technique. The derived criteria, which are expressed in terms of a set of LMIs, are delay‐distribution‐dependent, that is, the solvability of the criteria depends on not only the variation range of the delay but also the probability distribution of it. Finally, three numerical examples are given to illustrate the feasibility and effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

Fast adaptive fault estimation and accommodation for nonlinear time‐varying delay systems

This paper studies the problem of fault estimation and accommodation for a class of nonlinear time‐varying delay systems using adaptive fault diagnosis observer (AFDO). A novel fast adaptive fault estimation algorithm that does not need the derivative of the output vector is proposed to enhance the performance of fault estimation. Meanwhile, a delay‐dependent criteria is obtained based on free weighting matrix method with the purpose of reducing the conservatism of the AFDO design. On the basis of fault estimation, an observer‐based fault‐tolerant controller is designed to guarantee the stability of the closed‐loop system. In terms of matrix inequality, we derive sufficient conditions for the existence of the adaptive observer and fault‐tolerant controller. Simulation results are presented to illustrate the efficiency of the proposed method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

An LMI approach to robust fault estimation for a class of nonlinear systems

The paper presents a robust fault estimation approach for a class of nonlinear discrete‐time systems. In particular, two sources of uncertainty are present in the considered class of systems, that is, an unknown input and an exogenous external disturbance. Thus, apart from simultaneous state and fault estimation, the objective is to decouple the effect of an unknown input while minimizing the influence of the exogenous external disturbance within the framework. The resulting design procedure guarantees that a prescribed disturbance attenuation level is achieved with respect to the state and fault estimation error while assuring the convergence of the observer. The core advantage of the proposed approach is its simplicity by reducing the fault estimation problem to matrix inequalities formulation. In addition, the design conditions ensure the convergence of the observer with guaranteed performance. The effectiveness of the proposed approach is demonstrated by its application to a twin rotor multiple‐input multiple‐output system. Copyright © 2015 John Wiley & Sons, Ltd.     

Parity Relation Based Fault Estimation for Nonlinear Systems： An LMI Approach

This paper proposes a parity relation based fault estimation for a class of nonlinear systems which can be modelled by Takagi-Sugeno （TS） fuzzy models. The design of a parity relation based residual generator is formulated in terms of a family of linear matrix inequalities （LMIs）. A numerical example is provided to illustrate the effectiveness of the proposed design techniques.     

Delay‐dependent robust H∞ control for uncertain stochastic time‐delay systems

This paper investigates the robust H_∞ control problem for stochastic systems with a delay in the state. Sufficient delay‐dependent conditions for the existence of state‐feedback controllers are proposed to guarantee mean‐square asymptotic stability as well as the prescribed H_∞ performance for the closed‐loop systems. Moreover, the results are further extended to the stochastic time‐delay systems with parameter uncertainties, which are assumed to be time‐varying norm‐bounded appearing in both the state and the input matrices. The appealing idea is to partition the delay, which differs greatly from the most existing results and reduces conservatism by thinning the delay partitioning. Numerical examples are provided to show the advantages of the proposed techniques. Copyright © 2009 John Wiley & Sons, Ltd.     

Delay‐range‐dependent robust stability and stabilization for uncertain systems with time‐varying delay

This paper concerns delay‐range‐dependent robust stability and stabilization for time‐delay system with linear fractional form uncertainty. The time delay is assumed to be a time‐varying continuous function belonging to a given range. On the basis of a novel Lyapunov–Krasovskii functional, which includes the information of the range, delay‐range‐dependent stability criteria are established in terms of linear matrix inequality. It is shown that the new criteria can provide less conservative results than some existing ones. Moreover, the stability criteria are also used to design the stabilizing state‐feedback controllers. Numerical examples are given to demonstrate the applicability of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.     

Delay‐dependent state estimation for discrete Markovian jump neural networks with time‐varying delay

The state estimation problem is discussed for discrete Markovian jump neural networks with time‐varying delays in terms of linear matrix inequality (LMI) approach. The considered transition probabilities are assumed to be time‐variant and partially unknown. The aim of the state estimation problem is to design a state estimator to estimate the neuron states and ensure the stochastic stability of the error‐state system. A delay‐dependent sufficient condition for the existence of the desired state estimator is proposed. An explicit expression of the desired estimator is also given. A numerical example is introduced to show the effectiveness of the given result. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Delay‐dependent fault‐tolerant controller for time‐delay systems with randomly occurring uncertainties

This paper addresses the passivity‐based control problem for a class of time‐varying delay systems subject to nonlinear actuator faults and randomly occurring uncertainties via fault‐tolerant controller. More precisely, the uncertainties are described in terms of stochastic variables, which satisfies Bernoulli distribution, and the existence of actuator faults are assumed not only linear but also nonlinear, which is a more general one. The main objective of this paper is to design a state feedback‐reliable controller such that the resulting closed‐loop time‐delay system is stochastically stable under a prescribed mixed and passivity performance level γ>0 in the presence of all admissible uncertainties and actuator faults. Based on Lyapunov stability method and some integral inequality techniques, a new set of sufficient conditions is obtained in terms of linear matrix inequality (LMI) constraints to ensure the asymptotic stability of the considered system. Moreover, the control design parameters can be computed by solving a set of LMI constraints. Finally, two examples including a quarter‐car model are provided to show the efficiency and usefulness of the proposed control scheme. Copyright © 2017 John Wiley & Sons, Ltd.     

Delay‐range‐dependent control of nonlinear time‐delay systems under input saturation

This paper describes a delay‐range‐dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time‐delay systems under input saturation. By employing a Lyapunov–Krasovskii functional, properties of nonlinear functions, local sector condition and Jensen's inequality, a sufficient condition is derived for stabilization of nonlinear systems with interval delays varying within a range. Novel solutions to the delay‐range‐dependent and delay‐dependent stabilization problems for linear and nonlinear time‐delay systems, respectively, subject to input saturation are derived as specific scenarios of the proposed control strategy. Also, a delay‐rate‐independent condition for control of nonlinear systems in the presence of input saturation with unknown delay‐derivative bound information is established. And further, a robust state feedback controller synthesis scheme ensuring L₂ gain reduction from disturbance to output is devised to address the problem of the stabilization of input‐constrained nonlinear time‐delay systems with varying interval lags. The proposed design conditions can be solved using linear matrix inequality tools in connection with conventional cone complementary linearization algorithms. Simulation results for an unstable nonlinear time‐delay network and a large‐scale chemical reactor under input saturation and varying interval time‐delays are analyzed to demonstrate the effectiveness of the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd.     

Observer‐based Adaptive fuzzy control of time‐delay uncertain nonlinear systems

An observer‐based adaptive fuzzy model following controller is proposed for a class of MIMO nonlinear uncertain systems to cope with time‐delay, uncertainty in plant structure and disturbances. Based on universal approximation theorem the unknown nonlinear functions are approximated by fuzzy systems, where the premise and the consequent parts of the fuzzy rules are tuned with adaptive schemes. To have more robustness, and at the same time to alleviate chattering, an adaptive discontinuous structure is suggested. Moreover, the availability of the states measurement is not required and an adaptive observer is used to estimate the states. Asymptoic stability of the overall system is ensured using suitable a Lyapunov‐Krasovskii functional candidate. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Observer‐based fault estimators using iterative learning scheme for nonlinear time‐delay systems with intermittent faults

This paper deals with the intermittent fault estimation problem for a class of nonlinear time‐delay systems with measurement noise. The time delays are assumed to occur in state vector, nonlinear term as well as output vector, thus reflecting the time delays influence in reality more closely. The aim of the problem is to estimate the intermittent fault by using iterative learning scheme, with the property of index, hence attenuating the influence from measurement noise. Different from existing fault estimating schemes, the state error information and fault estimating information in the previous iteration are used in the current iteration to improve the estimating results. The stability and convergence of iterative learning observer and uniform boundedness of dynamic error system are achieved by using Lyapunov function and optimal function design. Simultaneously, an improved sufficient condition for the existence of such an estimator is established in terms of the linear matrix inequality by the Schur complements and Young relations. Furthermore, the results are both suited for the systems with time‐varying delay and the systems with constant delay. Finally, two numerical examples are proposed to illustrate the effectiveness of the proposed method, and a comparability example is presented to demonstrate its superiority. Copyright © 2017 John Wiley & Sons, Ltd.     

Delay‐range‐dependent bounded real lemma for time‐delay systems

In this paper, Bounded Real Lemma (BRL) for linear systems with time‐varying delay in a range is described. Unlike previous results, the low bound of the range is not restricted to be 0. Based on a new Lyapunov‐Krasovskii functional, a delay‐range‐dependent BRL is obtained in term of linear matrix inequality. It is shown that this new BRL can provide less conservative results than some existing ones. When time‐varying linear fractional form uncertainties appear in the delay system, a robust delay‐range‐dependent BRL is also given. Numerical examples are given to demonstrate the applicability of the proposed approach. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Delay‐dependent stability and stabilization of neutral time‐delay systems

This paper is concerned with the problem of stability and stabilization of neutral time‐delay systems. A new delay‐dependent stability condition is derived in terms of linear matrix inequality by constructing a new Lyapunov functional and using some integral inequalities without introducing any free‐weighting matrices. On the basis of the obtained stability condition, a stabilizing method is also proposed. Using an iterative algorithm, the state feedback controller can be obtained. Numerical examples illustrate that the proposed methods are effective and lead to less conservative results. Copyright © 2008 John Wiley & Sons, Ltd.     

Delay‐dependent conditions for finite time stability of linear time‐varying systems with delay

This paper investigates the problem of finite time stability of linear time‐varying system with delay. By constructing an augmented time‐varying Lyapunov functional and using the Wirtinger‐type inequality deductively, delay‐dependent finite time stability conditions are derived and presented in terms of differential linear matrix inequalities (DLMIs). Then, the DLMIs are transformed into a series of recursive linear matrix inequalities (RLMIs) by discretizing the time interval into equally spaced time distances, and an algorithm is given to solve the RLMIs. Examples illustrate the feasibility and effectiveness of the proposed method.     

An LMI approach to output‐feedback‐guaranteed cost control for uncertain time‐delay systems

This paper considers the problem of output‐feedback‐guaranteed cost controller design for uncertain time‐delay systems. The uncertainty in the system is assumed to be norm‐bounded and time‐varying. The time‐delay is allowed to enter the state and the measurement equations. A linear quadratic cost function is considered as a performance measure for the closed‐loop system. Necessary and sufficient conditions are provided for the construction of a guaranteed cost controller. These conditions are given in terms of the feasibility of LMIs which depend on a positive definite matrix and a scaling variable. A numerical algorithm is developed to search for a full order dynamic output‐feedback controller which minimizes the cost bound. Copyright © 2000 John Wiley & Sons, Ltd.     

Delay‐dependent robust stability for stochastic time‐delay systems with polytopic uncertainties

This paper considers a delay‐dependent and parameter‐dependent robust stability criterion for stochastic time‐delay systems with polytopic uncertainties. The delay‐dependent robust stability criterion, as expressed in terms of linear matrix inequalities (LMIs), is obtained by using parameter‐dependent Lyapunov functions. It is shown that the result derived by a parameter‐dependent Lyapunov functional is less conservative. Numerical examples are provided to illustrate the effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

An output delay approach to fault estimation for sampled-data systems

The problem of fault estimation for a class of non-uniformly sampled-data systems is investigated from the time delay point of view in this paper.Firstly,the output delay approach is employed to model the sampled-data system as a continuous-time one with time-varying delay output.Then,based on the analysis of the inapplicability of the adaptive fault diagnosis observer in such class of time-delay systems,a novel augmented fault estimation observer design method is proposed to guarantee the exponential convergence of the estimation errors.Furthermore,an extension to the case of time varying fault estimation for the noisy sampled-data systems is studied.Finally,simulation results of a flight control system are presented to demonstrate the effectiveness of the proposed method.     

Recursive observer‐based fault detection for a class of nonlinear uncertain systems with output constraints

This paper investigates the fault detection (FD) problem for a class of nonlinear uncertain systems in strict feedback form with an output constraint. The key idea is to design an observer to generate the FD signals and the output estimate, which also satisfies the output constraint. To facilitate constraint handling, the constraints on the output and the output estimate are transformed into the output estimation error constraint. Then, the FD observer is designed in a recursive framework. By employing a barrier Lyapunov function, the output estimation error constraint is incorporated in the last step of the recursive observer design algorithm to prevent constraint violation. It is shown that the output estimation error is uniformly bounded and satisfies the constraint for the fault‐free case. Furthermore, the residual signal is constructed by the output estimation error, and its corresponding bound is used as threshold. Compared with the FD method without considering the constraints, the proposed FD scheme provides a smaller threshold and characterizes a larger set of faults, which can be detected. Finally, simulation results are presented to illustrate the benefits of the proposed FD scheme. Copyright © 2016 John Wiley & Sons, Ltd.