Adaptive fault tolerant control design for Takagi–Sugeno fuzzy systems with interval time‐varying delay

This paper deals with the problem of fault‐tolerant control (FTC) of continuous‐time Takagi–Sugeno fuzzy systems with interval time‐varying delay by using adaptive observer. Through constructing an appropriate type of Lyapunov function, a delay‐dependent criterion is established to reduce the conservatism of designing an active FTC (AFTC). In comparison with the existing techniques in the literature, the proposed approach simplifies the design of an AFTC and gives in only one step of the estimate of state vector, the estimate of actuator fault and the controller gains. Some simulation examples are included to demonstrate the effectiveness of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.     

Stochastic faulty actuator‐based reliable control for a class of interval time‐varying delay systems with Markovian jumping parameters

The paper addresses the problem of a reliable control for interval time‐varying delay system with Markovian jumping parameters. A new practical actuator fault model, by assuming that the actuator fault obeys a certain probabilistic distribution, is considered. Delay‐dependent conditions for the solvability of these problems are obtained via new parameter‐dependent Lyapunov function. The closed‐loop systems are stochastically stable not only when all actuators are operational, but also in case of some actuator failures. Numerical examples are given to illustrate the effectiveness of the proposed design method. Copyright © 2010 John Wiley & Sons, Ltd.     

Stability criteria for continuous‐time systems with additive time‐varying delays

This paper studies the problem of stability analysis for continuous‐time systems with two additive time‐varying delay components. By taking the independence and the variation of the additive delay components into consideration, more general type of Lyapunov functionals are defined. Together with a tighter estimation of the upper bound of the cross‐product terms derived from the derivatives of the Lyapunov functionals, less conservative delay‐dependent stability criteria are established in terms of LMIs. Combining with a reciprocally convex combination technique, the newly obtained stability conditions are also less complex. Two numerical examples are given to illustrate the effectiveness and the significant improvement of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Observer‐based actuator fault estimation and proportional derivative fault tolerant control for continuous‐time singular systems

This paper focuses on designing fault estimation (FE) and fault tolerant control (FTC) schemes for continuous‐time singular systems affected by actuator fault. A novel observer called the extended proportional integral observer (PIO) is designed so that the estimations of system state and actuator fault can be obtained simultaneously. In contrast with the traditional PIO, better estimation performance can be obtained by using the designed observer. Furthermore, with the obtained FE information, a novel proportional derivative–type FTC scheme is given by means of the separation property and the free‐weighting matrix technique, which ensures that the closed‐loop system is normal and stable. All the feasible conditions are formulated in linear matrix inequality (LMI) frameworks. Finally, two examples are simulated to prove the superiority and practicability of the presented scheme.     

Set‐valued observer‐based active fault‐tolerant model predictive control

This paper proposes an integrated actuator and sensor active fault‐tolerant model predictive control scheme. In this scheme, fault detection is implemented by using a set‐valued observer, fault isolation (FI) is performed by set manipulations, and fault‐tolerant control is carried out through the design of a robust model predictive control law. In this paper, a set‐valued observer is used to passively complete the fault detection task, while FI is actively performed by making use of the constraint‐handling capability of robust model predictive control. The set‐valued observer is chosen to implement fault detection and isolation (FDI) because of its simple mathematical structure that is not affected by the type of faults such as sensor, actuator, and system‐structural faults. This means that only one set‐valued observer is needed to monitor all considered actuator and sensor statuses (health and fault) and to carry out the fault detection and isolation task instead of using a bank of observers (each observer matching a health/fault status). Furthermore, in the proposed scheme, the advantage of robust model predictive control is that it can effectively deal with system constraints, disturbances, and noises and allow to implement an active FI strategy, which can improve FI sensitivity when compared with the passive FI methods. Finally, a case study based on the well‐known two‐tank system is used to illustrate the effectiveness of the proposed fault‐tolerant model predictive control scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

Further results on H ∞ control for discrete‐time uncertain singular systems with interval time‐varying delays in state and input

This paper investigates the state feedback robust H _∞ control problem of a class of discrete‐time singular systems with norm‐bounded uncertainties and interval time‐varying delays in state and input. A new bounded real lemma for discrete‐time singular systems with a pair of time‐varying interval state delays is first investigated. Mathematical comparisons of the new bounded real lemma and two existing ones are presented. Then, on the basis of the bounded real lemma proposed here, a sufficient condition in the form of nonlinear matrix inequality, such that the considered state feedback robust H _∞ control problem is solvable, is given. In order to solve the nonlinear matrix inequality, a cone complementarity linearization algorithm is offered. Several numerical examples are presented to show the applicability of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust reliable control for discrete‐time‐delay systems with stochastic nonlinearities and multiplicative noises

This paper is concerned with the reliable control problem against actuator failures for a class of uncertain discrete‐time stochastic nonlinear time‐delay systems. The failures of actuators are quantified by a variable varying in a given interval. The stochastic nonlinearities described by statistical means cover several well‐studied nonlinear functions as special cases. The time‐varying delay is unknown with given lower and upper bounds. The multiplicative stochastic disturbances are in the form of a scalar Gaussian white noise with unit variance. Attention is focused on the analysis and design of a stable controller such that, for all possible actuator failures, stochastic nonlinearities and disturbances, time delays and admissible parameter uncertainties, the closed‐loop system is exponentially mean‐square stable. A linear matrix inequality approach is developed to solve the addressed problem. A numerical example is given to demonstrate the effectiveness of the proposed design approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust H∞ guaranteed cost control for discrete‐time switched singular systems with time‐varying delay

This paper investigates the problem of control design for a class of uncertain switched singular systems with time‐varying delay. Under mode‐dependent average dwell time and using an appropriate Lyapunov‐Krasovskii functional, the exponential admissibility of the system is analyzed. In order to obtain less conservative conditions, the delay partitioning technique is adopted as well as the improved reciprocally convex approach. By means of the developed admissibility condition, a static output feedback controller is then designed using linear matrix inequality approach. Moreover, by solving an optimization convex problem with constraints, the switched controller is developed to ensure simultaneously the stability of the closed‐loop system and satisfy an optimized upper bound of both the linear quadratic guaranteed cost and the H_∞ norm. Numerical examples are proposed to verify the efficiency and the merits of the method proposed.     

Multiobjective fault‐tolerant fixed‐order/PID control of multivariable discrete‐time linear systems with unmeasured disturbances

In this paper, a multiobjective fault‐tolerant fixed‐order output feedback controller design technique is proposed for multivariable discrete‐time linear systems with unmeasured disturbances. Initially, a multiobjective fixed‐order controller is designed for the system by transforming the problem of tuning the parameters of the controller into a static output feedback problem and solving a mixed H₂/H_∞ optimization problem with bilinear matrix inequalities. Subsequently, the fixed‐order controller is used to construct the closed‐loop system and an active fault‐tolerant control scheme is applied using the input/output data collected from the controlled system. Motivated by its popularity in industry, the proposed method is also used to tune the parameters of proportional‐integral‐derivative controllers as a special case of structured controllers with the fixed order. Two numerical simulations are provided to demonstrate the design procedure and the flexibility of the proposed technique.     

Improved reachable set estimation of discrete‐time systems with time‐varying delay

This paper is concerned with the problem of reachable set estimation of discrete‐time systems with time‐varying delay and bounded disturbance. By applying the improved reciprocally convex combination approach to bound the forward difference of the double summation and triple summation, respectively, a less conservative reachable set estimation condition is developed in matrix inequalities. Based on the criterion, a less conservative stability criterion is obtained as a by‐product. Numerical examples are presented to validate the effectiveness of the obtained results.     

Improved delay‐partitioning approach to robust stability analysis for discrete‐time systems with time‐varying delays and randomly occurring parameter uncertainties

This paper is concerned with the robust stability problem for uncertain discrete‐time systems with interval time‐varying delays and randomly occurring parameter uncertainties. By construction of a suitable Lyapunov–Krasovskii functional and utilization of new zero equalities with delay‐partitioning approach, improved delay‐dependent criteria for the robust stability of the systems are derived in terms of linear matrix inequalities for guaranteeing the asymptotic stability of the concerned systems. The effectiveness and reduction of conservatism of the derived results are demonstrated by three numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.     

Delay‐dependent robust passive control for a class of nonlinear systems with time‐varying delays

In this paper, the problem of robust passive control for a class of nonlinear systems with time‐varying delays is considered. The uncertainties investigated in this paper are norm bounded and time varying, and they enter all system matrices. Based on the Lyapunov–Krasovskii functionals approach, a new robust passive control criterion is proposed in terms of linear matrix inequalities, which is dependent on the size of time delay. We also design a state feedback controller that guarantees a robust asymptotically stable and strictly passive closed‐loop system for all admissible uncertainties. Finally, two numerical examples are given to illustrate the effectiveness of the developed techniques. Copyright © 2007 John Wiley & Sons, Ltd.     

Reliable control for interval time‐varying delay systems subjected to actuator saturation and stochastic failure

This paper is devoted to the problem of reliable control for interval time‐varying delay systems subjected to actuator saturation and stochastic failure. A new practical actuator fault model is proposed by assuming that the actuator fault obeys a certain probabilistic distribution. An optimization problem with LMI constraints is formulated to determine the largest contractively invariant ellipsoid. Delay distribution and fault distribution‐dependent estimations of the domain of attraction are obtained by using the LMI techniques and an optimization method, such that the mean‐square stability of the systems can be guaranteed for given H_∞ performance index γ. Two illustrative examples are exploited to show the effectiveness of the proposed design procedures. Copyright © 2011 John Wiley & Sons, Ltd.     

Stochastic control of networked control systems with packet dropout and time‐varying delay

This paper studies the stochastic stabilization problem for discrete‐time networked control systems with time delay and packet dropout. The message losses and time delay from the sensor to the controller and from the controller to the actuator are considered simultaneously. A two‐state Markov chain is used to model the correlated packet dropout process. By introducing free weighting matrices, the sufficient condition on the stochastic stability of such networked control system is obtained. An improved criterion is found by introducing the delay fractioning method and a new Lyapunov–Krasovskii functional. On the basis of the stability condition, the mode‐dependent controller is given in terms of linear matrix inequalities. A simulation example is given to show the proposed results. Copyright © 2012 John Wiley & Sons, Ltd.     

Stability analysis and observer design for discrete‐time systems with interval time‐varying delay

The problem of observer design for a class of nonlinear discrete‐time systems with time‐varying delay is considered. A new approach of nonlinear observer design is proposed for the class of systems. By using Lyapunov's stability theory and Schur complement lemma, the novel sufficient conditions that guarantee the observer error converge asymptotically to zero are obtained in terms of linear matrix inequalities. The computing method for observer gain matrix is given. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

Reduced‐order observer‐based fault estimation and fault‐tolerant control for a class of discrete Lipschitz nonlinear systems

This paper addresses an issue on reduced‐order observer‐based robust fault estimation and fault‐tolerant control for a class of uncertain nonlinear discrete‐time systems. By introducing a nonsingular coordinate transformation, a new nonlinear reduced‐order fault estimation observer (RFEO) is proposed with a wide application range in order to achieve an accurate estimation of both states and faults. Next, an improved algorithm is given to obtain the optimal estimation by using a novel iterative linear matrix inequality technique. Furthermore, an RFEO‐based output feedback fault‐tolerant controller, which is independent of the RFEO, can maintain the stability and performance of the faulty system. Simulation results of an aircraft application show the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust H∞ performance analysis for uncertain discrete‐time singular systems with time‐varying delays

This paper considers the problem of robust H∞ performance analysis for uncertain discrete‐time singular systems with time‐varying delays. Firstly, a delay‐dependent stability criterion under the H∞ performance index for the systems is given based on constructing a generalized Lyapunov–Krasovskii function and introducing a new difference inequality. Then, a sufficient condition ensuing the system to be regular, causal as well as stable for all admissible uncertainties is proposed in terms of a set of strict linear matrix inequalities (LMIs). Finally, we provide examples to show the reduced conservatism and effectiveness of the proposed conditions. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust reliable guaranteed cost control for uncertain T‐S fuzzy neutral systems with interval time‐varying delay and linear fractional perturbations

The robust reliable guaranteed cost control for Takagi–Sugeno fuzzy systems with interval time‐varying delay is considered in this paper. Some free weighting matrices and non‐negative terms are provided to improve the conservativeness of our main results. An LMI optimization approach is applied to solve the problems of robust reliable guaranteed cost control and minimization of cost function. Copyright © 2014 John Wiley & Sons, Ltd.