H2 filter design for discrete‐time Markov jump linear systems with partly unknown transition probabilities

The H₂ filter design problem for discrete‐time Markov jump linear systems with partly unknown transition probabilities is addressed in this paper. The so‐called partly unknown transition probabilities cover two cases: one is that some unknown elements have known lower and upper bounds, the other is that some unknown elements have no information available. By employing Finsler's lemma and linear matrix inequality (LMI) technique, sufficient conditions are developed in the LMI setting to design an H₂ filter such that the filtering error system is mean‐square stable and at the same time satisfies a prescribed H₂ performance index. Numerical examples are presented to illustrate the effectiveness of the developed theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

A robust control system scheme based on model predictive controller (MPC) for continuous‐time systems

In this paper, an LMI framework based on model predictive strategy is addressed to design a robust dynamical control law in a typical control system. In the proposed method, instead of traditional static controller, a dynamic control law is used. With a suitable matrix transformation, the controller parameters selection are translated into an optimization problem with some LMI constraints. The plant input and output constraints are also handled with another LMIs. The controller is represented in state space form, and its parameters are computed in real‐time operation. For achieving this goal, by solving an optimization problem, a dynamic controller is designed, which meets the required plant performances. These results are used in 2 numerical examples to demonstrate the effectiveness of the proposed approach.     

H∞ control of switched linear discrete‐time systems with polytopic uncertainties

In this paper, the problem of designing H_∞ state‐feedback controllers for switched linear discrete‐time systems with polytopic uncertainties is investigated. Two approaches on designing robust and parameter‐dependent H_∞ controllers are proposed and the existence conditions of the desired controllers are derived and formulated in terms of a set of linear matrix inequalities. By solving the corresponding convex optimization problem, the desired controllers are obtained, respectively, and different optimal H_∞ noise‐attenuation level bounds of corresponding closed‐loop systems are given as well. The designed controllers have their own advantages and disadvantages regarding the conservatism and realization complexity. An illustrative example emerging in networked control systems (NCS) and numerical simulations are presented to show the applicability and effectiveness of the obtained theoretic results. Copyright © 2006 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.     

Nonfragile reliable control for positive switched systems with actuator faults and saturation

This paper presents a nonfragile reliable control approach to positive switched systems with actuator faults and saturation. In order to guarantee the reliability of the controller, the controller gain matrix is chosen as the sum of a normal gain matrix and a gain perturbation matrix. A nonfragile reliable control is first proposed for the considered systems using a gain matrix decomposition technique. Then, the presented nonfragile control design approach is developed for the systems with exogenous disturbances. An approach to compute the normal gain matrix and the gain perturbation matrix is also provided. Under the obtained controller, the resulting closed‐loop systems are positive and L₁‐gain stable. Meanwhile, all the states will stay inside a cone. All presented conditions are described via linear programming. Finally, two examples are provided to verify the effectiveness of the theory findings.     

Optimal guaranteed cost for singular linear systems with random abrupt changes

This paper considers the class of continuous‐time singular linear Markovian jump systems with totally and partially known transition jump rates. The guaranteed cost control problem of this class of systems is tackled. New sufficient conditions for optimal guaranteed cost are developed. A design procedure for the guaranteed cost controller, which guarantees that the closed‐loop dynamics will be piecewise regular, impulse‐free and stochastically stable is proposed. It is shown that the addressed problem can be solved if the corresponding developed linear matrix inequalities (LMIs) with some constraints are feasible. A numerical example is employed to show the usefulness of the proposed results. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust fault detection for networked control systems with packet dropouts: An average dwell time method

The problem of fault detection for networked control systems with respect to packet dropouts is investigated in this paper based on average dwell time method. For the cases that there may be sensor stuck failure and packet dropouts, the networked control systems are modeled as discrete time switched systems. Subsequently, a novel fault detection scheme, which is valid to detect the failures with small magnitudes even the outage ones, is proposed by making the generated residuals sensitive to servo inputs in faulty cases and robust against it in normal case. By utilizing the average dwell time method, new sufficient conditions, which include some existing results, for characterizing the sensitivity performance and the attenuation performance are presented in terms of linear matrix inequalities. Meanwhile, the relation between the packet dropout rate and the system performance is established. Finally, an application of a linearized aircraft is given to demonstrate the effectiveness of the proposed results. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust finite-time control and estimation for uncertain time-delayed switched systems by observer-based sliding mode technique

This article investigates the robust estimation and observer-based finite time sliding mode control problems for a class of switched systems with time-delays and uncertainties. For the studied system model, a common sliding surface related to the estimated states is initially constructed. Then, a suitable sliding mode control law is designed to ensure the accessibility of sliding surface. By selecting the appropriate Lyapunov function and using the average dwell time method and the partition strategy lemma, sufficient conditions of finite time boundedness of system are given. The observer gain is obtained by solving a couple of linear matrix inequalities. Finally, a practical water quality control system is given to show the effectiveness of the design methods.     

An inverse dynamics-based dynamic programming method for optimal control problems of linear systems

In solving optimal control problems, the conventional dynamic programming method often requires interpolations to determine the optimal control law. As a consequence, interpolation errors often degenerate the accuracy of the conventional dynamic programming method. In view of this problem, this paper introduces an inverse dynamics-based dynamic programming method to eliminate the interpolation requirement for systems with linear dynamics. Simulation results show that the proposed approach provides more reliable solutions than the conventional dynamic programming method. Copyright © 1998 John Wiley & Sons, Ltd.     

A µ‐dependent approach to H∞ control of uncertain switched linear systems with average dwell time

This paper concerns H_∞ control problem for a class of discrete‐time uncertain switched linear systems with average dwell time. The stability result for general discrete‐time switched systems is first explored, and a µ‐dependent approach is then introduced for the considered systems to the H_∞ controller solution. A mode‐dependent state‐feedback controller is designed such that the resulting closed‐loop system is robust exponentially stable and has a prescribed exponential H_∞ performance index. The µ‐dependent existence conditions of desired controller and admissible switching signals are derived and formulated in terms of linear matrix inequalities (LMIs). A numerical example is given to demonstrate the effectiveness of the developed theoretical results. Copyright © 2009 John Wiley & Sons, Ltd.     

A framework of robust fault estimation observer design for continuous‐time/discrete‐time systems

A design framework of the observer‐based robust fault estimation for continuous‐time/discrete‐time systems is presented in this paper. Firstly, a multiconstrained fault estimation observer under the H_∞ performance specification with the regional pole constraint is proposed to achieve robust fault estimation. Then, the existence conditions for both continuous‐time/discrete‐time systems are derived explicitly. Furthermore, by introducing slack variables, improved results on the multiconstrained fault estimation observer design are obtained such that different Lyapunov functions can be separately designed for each constraint. Finally, simulation results of a vertical takeoff and landing aircraft are presented to illustrate our contributions. Copyright © 2012 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.     

Time‐delay dependent H∞ model simplification for singular systems with Markovian jumping parameters

The problem of H_∞ model simplification for singular systems with Markovian jumping parameters and time‐delay is investigated. For a given stochastic stable system, our attention is focused on the construction of reduced‐order models which guarantee the corresponding error system to be admissible and have a prescribed H_∞ error performance. A robust admissibility condition and a robust bounded real lemma are developed based on which, sufficient conditions for the existence of desired reduced‐order models are proposed. Desired reduced‐order model can be constructed when the proposed conditions are satisfied. The effectiveness of the proposed model reduction method is illustrated via a numerical example. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Exponential stability analysis for 2D discrete switched systems with state delays

This paper is concerned with the delay‐dependent exponential stability analysis of two‐dimensional (2D) discrete switched systems with state delays described by the Roesser model; the delays under consideration are varying. By constructing an appropriate Lyapunov‐Krasovskii functional and using the average dwell time approach, new delay‐dependent sufficient conditions for the exponential stability of the system under study are proposed. In order to obtain less conservative conditions, the delay partitioning method is adopted as well as the free‐weighting matrix technique. The proposed conditions are formulated in the format of linear matrix inequality. The effectiveness and the reduced conservatism of the developed results are shown by illustrative examples.     

Robust H∞ control for switched singular linear systems with uncertainties in the derivative matrices: an improved average dwell time approach

This paper addresses the robust H_∞ control problem for continuous‐time switched singular systems with uncertainties in the state, input, and derivative matrices. A two‐phase method is proposed in this paper to optimize H_∞ performance and to minimize the upper bound of the average dwell time. First, sufficient conditions for finding a state feedback controller guaranteeing the minimum H_∞ disturbance attenuation are proposed. Besides, the average dwell time is obtained by solving linear matrices inequalities introduced in this paper. Second, to minimize the upper bound of the average dwell time, an improve average dwell time approach is put forward by introducing a new technique. And based on the result in the first phase, a new feedback controller, which optimizes H_∞ performance and minimizes the upper bound of the average dwell time is obtained by using the improved average dwell time approach. The point is that when the upper bound of the average dwell time is decreasing, H_∞ disturbance attenuation will increase and vice versa. Therefore, a trade‐off should be built between H_∞ disturbance attenuation and average dwell time in practice. Finally, several numerical examples are presented to illustrate the effectiveness of the methods proposed. Copyright © 2015 John Wiley & Sons, Ltd.     

H∞ control for linear switched systems with time‐varying delay and dead‐zone inputs via an adaptive memory controller

This paper deals with the problem of robust H_∞ control for linear switched systems with time‐varying delay and dead‐zone inputs. First, a new state‐dependent switching law is proposed for the switched system with stable and unstable subsystems. Based on the proposed switching law and using the scaled small gain theorem, a more general stability criterion for the switched delay systems is established. Second, an adaptive memory controller is proposed for the switched system with dead‐zone inputs. With the help of a two‐term approximation of the time‐varying delay, the proposed memory controller only depends on the bounds of the time‐varying delay. Sufficient conditions on the existence of the desired controller are formulated in terms of linear matrix inequalities. Three examples are provided to illustrate the effectiveness of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust H∞ control for uncertain linear neutral delay systems

This paper deals with the problem of robust H_∞ control for uncertain linear neutral delay systems. The parameter uncertainty under consideration is assumed to be norm‐bounded time‐invariant and appears in all the matrices of the state‐space model. The problem we address is the design of memoryless state feedback controllers such that the closed‐loop system is asymptotically stable and the H_∞ norm of the closed‐loop transfer function from disturbance to the controlled output is strictly less than a prescribed positive scalar for all admissible uncertainties. In terms of a linear matrix inequality (LMI), a sufficient condition for the solvability of the above problem is proposed. When this matrix inequality is feasible, an explicit expression for the desired state feedback controller is given. Furthermore, a numerical example is provided to demonstrate the effectiveness of the proposed approach. Copyright © 2002 John Wiley & Sons, Ltd.