H∞ filtering for continuous‐time singular systems with time‐varying delay

This paper focuses on H_∞ filter design for continuous‐time singular systems with time‐varying delay. A delay‐dependent H_∞ performance analysis result is first established for error systems via a novel estimation method. By combining a well‐known inequality with a delay partition technique, the upper bound of the derivative of the Lyapunov functional is estimated more tightly and expressed as a convex combination with respect to the reciprocal of the delay rather than the delay. Based on the derived H_∞ performance analysis results, a regular and impulse‐free H_∞ filter is designed in terms of linear matrix inequalities (LMIs). A numerical example is given to demonstrate the merits of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

Fault detection filter design for discrete‐time switched linear systems with mode‐dependent average dwell‐time

This paper is concerned with the problem of the fault detection (FD) filter design for discrete‐time switched linear systems with mode‐dependent average dwell‐time. The switching law is mode‐dependent and each subsystem has its own average dwell‐time. The FD filters are designed such that the augmented switched systems are asymptotically stable, and the residual signal generated by the filters achieves a weighted l₂‐gain for some disturbances and guarantees an H _? performance for the fault. By the aid of multiple Lyapunov functions combined with projection lemma, sufficient conditions for the design of the FD filters are formulated by linear matrix inequalities, furthermore, the filters gains are characterized in terms of the solution of a convex optimization problem. Finally, an application to boost convertor is given to illustrate the effectiveness and the applicability of the proposed design method. Copyright © 2013 John Wiley & Sons, Ltd.     

Exponential l2 − l∞ filtering for discrete‐time switched systems under a new framework

In this paper, a robust exponential l₂ ? l_∞ filtering problem is addressed for discrete‐time switched systems with polytopic uncertainties. The purpose of robust exponential l₂ ? l_∞ filtering is to design a filter such that the resulting filtering error system is robustly exponentially stable with a decay rate and a prescribed exponential l₂ ? l_∞ performance index. The robust exponential l₂ ? l_∞ filtering problem is solved via an average dwell time approach. Sufficient conditions in terms of strict LMI are derived for checking the robust exponential stability of a filter. An explicit expression for the desired robust exponential filter is also given. Finally, a numerical example is provided to demonstrate the potential and effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

Finite‐time H ∞ filtering for a class of discrete‐time Markovian jump systems with partly unknown transition probabilities

This paper is concerned with the problem of finite‐time H _∞ filtering for a class of Markovian jump systems subject to partial information on the transition probabilities. By introducing some slack matrix variables in terms of probability identity, a less conservative bounded real lemma is derived to ensure that filtering Markovian jump systems is finite‐time stable. Finally, the existence criterion of the desired filter is obtained such that the corresponding filtering error system is finite‐time bounded with a guaranteed H _∞ performance index. An example is given to illustrate the efficiency of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust H∞ filtering for switched linear discrete‐time systems with polytopic uncertainties

In this paper, the problem of robust H_∞ filtering for switched linear discrete‐time systems with polytopic uncertainties is investigated. Based on the mode‐switching idea and parameter‐dependent stability result, a robust switched linear filter is designed such that the corresponding filtering error system achieves robust asymptotic stability and guarantees a prescribed H_∞ performance index for all admissible uncertainties. The existence condition of such filter is derived and formulated in terms of a set of linear matrix inequalities (LMIs) by the introduction of slack variables to eliminate the cross coupling of system matrices and Lyapunov matrices among different subsystems. The desired filter can be constructed by solving the corresponding convex optimization problem, which also provides an optimal H_∞ noise‐attenuation level bound for the resultant filtering error system. A numerical example is given to show the effectiveness and the potential of the proposed techniques. Copyright © 2006 John Wiley & Sons, Ltd.     

Mixed and passive filtering for linear switched systems with average dwell time

In this paper, a new performance index is proposed for switched systems. The new performance index can be viewed as the mixed weighted and passivity performance. This new performance index covers the weighted performance and the passivity performance as special cases. Based on this new performance index, the weighted filtering problem and the passive filtering problem of linear switched systems with unstable subsystems are solved in a unified framework. The states of the filtering error system constructed by the augmentation technique will be divergent when unstable subsystems are activated. To overcome this problem, a set of mode‐dependent filters of a Luenberger‐like observer type is constructed. The multiple Lyapunov function approach and the average dwell‐time technique are employed to solve the mixed filtering problem. New sufficient conditions for the existence of mixed and passive filters are developed, which ensure the filtering error system to be asymptotically stable with a prescribed mixed and passivity performance index. Moreover, the desired mixed and passive filters can be constructed by solving a set of linear matrix inequalities. Finally, numerical examples are given to demonstrate the applicability and advantage of the obtained results.     

Fault estimation and tolerant control for discrete‐time switched systems with sojourn probabilities

This paper addresses the issue of fault estimation and accommodation for a discrete‐time switched system with actuator faults. Here, we assume that the sojourn probabilities are known a priori. By using the reduced‐order observer method, the sojourn probability approach, and the Lyapunov technique, a fault estimation algorithm is obtained for the considered system. The main objective of this work is to design a dynamic output feedback fault‐tolerant controller based on the obtained fault estimation information such that the closed‐loop discrete‐time switched system with available sojourn probabilities is robustly mean‐square stable and satisfies a prescribed mixed and passivity disturbance attenuation level in the presence of actuator faults. More precisely, a dynamic output feedback fault‐tolerant controller is established in terms of linear matrix inequalities. Finally, numerical examples are provided to illustrate the usefulness and effectiveness of the proposed design technique.     

filtering for switched discrete‐time systems under asynchronous switching: A dwell‐time dependent Lyapunov functional method

In this article, the filtering problem for switched discrete‐time linear systems under asynchronous switching is addressed in the framework of dwell time, where ‘asynchronous switching’ covers more general and practical cases, for example, the switching lags caused by mode identification process are taken into consideration. Firstly, a novel dwell‐time dependent Lyapunov function (DTDLF) is introduced to solve stability and ?₂ gain analysis problems. The main advantage of DTDLF approach is that the derived conditions are all convex in system matrices, so it is convenient to be applied into filter design with performance instead of weighted performance as many other previous results. Thus, on the basis of DTLDF, a dwell‐time dependent filter with time‐varying structure is proposed to achieve the desirable non‐weighted filtering performance. It is notable that the proposed approach can also easily characterize the relationships among filtering performance, dwell time, and asynchronous time. Two examples are provided to validate the theoretical findings in this paper. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust H ∞ filtering for a class of uncertain stochastic hybrid neutral systems with time‐varying delay

This paper is devoted to the problem of robust H _∞ filtering for a class of uncertain switched neutral systems subject to stochastic disturbance and time‐varying delay. Attention is focused on the design of a full‐order switched filter such that the filtering error system is robust mean‐square exponentially stable with a prescribed weighted H _∞ performance. On the basis of the average dwell time approach and the piecewise Lyapunov function technique, sufficient conditions for the solvability of this problem are obtained in terms of linear matrix inequalities. Then, by solving the corresponding linear matrix inequalities, the desired full‐order switched filter is derived for all admissible uncertainties, time‐varying delay, and stochastic disturbances. A numerical example is given to illustrate the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive robust H∞ state feedback control for linear uncertain systems with time‐varying delay

This paper considers the problem of adaptive robust H_∞ state feedback control for linear uncertain systems with time‐varying delay. The uncertainties are assumed to be time varying, unknown, but bounded. A new adaptive robust H_∞ controller is presented, whose gains are updating automatically according to the online estimates of uncertain parameters. By combining an indirect adaptive control method and a linear matrix inequality method, sufficient conditions with less conservativeness than those of the corresponding controller with fixed gains are given to guarantee robust asymptotic stability and H_∞ performance of the closed‐loop systems. A numerical example and its simulation results are given to demonstrate the effectiveness and the benefits of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

Sliding mode control of switched hybrid systems with time‐varying delay

This paper is concerned with the sliding mode control of a continuous‐time switched system with time‐varying delay in its state. By using the average dwell time approach and the piecewise Lyapunov function technique, a sufficient condition is first proposed to guarantee the exponential stability of the unforced system with the decay estimate explicitly given. A sufficient condition of the existence of a reduced‐order sliding mode dynamics is derived, and an explicit parametrization of the desired sliding surface is also given. The obtained conditions will be solved using the cone complementary linearization (CCL) method. An adaptive sliding mode controller for the reaching motion is then designed such that the trajectories of the resulting closed‐loop system can be driven onto a prescribed sliding surface and maintained there for all subsequent times. All the conditions obtained in this paper are delay dependent. Finally, two numerical examples are given to illustrate the effectiveness of the proposed theory. Copyright © 2008 John Wiley & Sons, Ltd.     

On robust H∞ filtering of uncertain Markovian jump time‐delay systems

This paper is concerned with the problems of stability analysis, H_∞ performance analysis, and robust H_∞ filter design for uncertain Markovian jump linear systems with time‐varying delays. The purpose is to improve the existing results on these problems. Firstly, a new delay‐dependent stability criterion is obtained on the basis of a novel mode‐dependent Lyapunov functional. Secondly, a new delay‐dependent bounded real lemma (BRL) is derived. It is shown that the presented stability criterion and the BRL are less conservative than the existing ones in the literature. Thirdly, with the new BRL, delay‐dependent conditions for the solvability of the addressed H_∞ filtering problem are given. All the results obtained in this paper are expressed by means of strict linear matrix inequalities. Three numerical examples are provided to demonstrate the utility of the proposed methods. Copyright © 2011 John Wiley & Sons, Ltd.     

Active fault‐tolerant control for switched systems with time delay

This paper focuses on the problem of active fault‐tolerant control for switched systems with time delay. By utilizing the fault diagnosis observer, an adaptive fault estimate algorithm is proposed, which can estimate the fault signal fast and exactly. Meanwhile, a delay‐dependent criterion is obtained with the purpose of reducing the conservatism of the adaptive observer design. Based on the fault estimation information, an observer‐based fault‐tolerant controller is designed to guarantee the stability of the closed‐loop system. In terms of linear matrix inequality, sufficient conditions are derived for the existence of the adaptive observer and fault‐tolerant controller. Finally, a numerical example is included to illustrate the efficiency of the proposed approach. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust learning controller design for MIMO stochastic discrete‐time systems: An H∞‐based approach

This paper is devoted to designing iterative learning control (ILC) for multiple‐input multiple‐output discrete‐time systems that are subject to random disturbances varying from iteration to iteration. Using the super‐vector approach to ILC, statistical expressions are presented for both expectation and variance of the tracking error, and time‐domain conditions are developed to ensure their asymptotic stability and monotonic convergence. It shows that time‐domain conditions can be tied together with an H_∞‐based condition in the frequency domain by considering the properties of block Toeplitz matrices. This makes it possible to apply the linear matrix inequality technique to describe the convergence conditions and to obtain formulas for the control law design. Furthermore, the H_∞‐based approach is shown applicable to ILC design regardless of the system relative degree, which can also be used to address issues of model uncertainty. For a class of systems with a relative degree of one, simulation tests are provided to illustrate the effectiveness of the H_∞‐based approach to robust ILC design. Copyright © 2011 John Wiley & Sons, Ltd.     

Delay‐dependent model reduction for continuous‐time switched state‐delayed systems

This paper studies the problem of exponential H_∞ model reduction for continuous‐time switched delay system under average dwell time (ADT) switching signals. Time delay under consideration is interval time varying. Our attention is focused on the construction of the desired reduced order models, which guarantee that the resulting error systems under ADT switching signals are exponentially stable with an H_∞ norm bound. By introducing a block matrix and making use of the ADT approach, delay‐dependent sufficient conditions for the existence of reduced order models are derived and formulated in terms of strict linear matrix inequalities (LMIs). Owing to the absence of non‐convex constraints, it is tractable to construct an admissible reduced order model. The effectiveness of the proposed methods is illustrated via two numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.     

Fault detection for a class of network‐based nonlinear systems with communication constraints and random packet dropouts

This paper is dealt with the fault detection (FD) problem for a class of network‐based nonlinear systems with communication constraints and random packet dropouts. The plant is described by a Takagi–Sugeno fuzzy time‐delay model, it has multiple sensors and only one of them is actually communicated with the FD filter at each transmission instant, and the packet dropouts occur randomly. The goal is to design a FD filter such that, for all unknown inputs, control inputs, time delays and incomplete data conditions, the estimation error between the residual and ‘fault’ (or, more generally, the weighted fault) is minimized. By casting the addressed FD problem into an auxiliary H_∞ filtering problem of a stochastic switched fuzzy time‐delay system, a sufficient condition for the existence of the desired FD filter is established in terms of linear matrix inequalities. A numerical example is provided to illustrate the effectiveness and applicability of the proposed technique. Copyright © 2011 John Wiley & Sons, Ltd.     

Fault detection filter design for networked control systems with time‐varying sampling periods and packet dropouts

This paper investigates the problem of fault detection for networked control systems under simultaneous consideration of time‐varying sampling periods and packet dropouts. By taking time‐varying sampling periods into consideration, a new closed‐loop model for the considered networked control systems is established. The sampling period switching‐based approach and the parameter uncertainty‐based approach are adopted to deal with time‐varying sampling periods. Based on the established model, the observer‐based fault detection filter design criteria are proposed to asymptotically stabilize the residual system in the sense of mean‐square. The designed observer‐based fault detection filter can guarantee the sensitivity of the residual signal to faults. The simulation results illustrate the effectiveness of the obtain results. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust observer‐based control design for uncertain singular systems with time‐delay

This paper is concerned with the stability analysis and robust dynamic output feedback controller synthesis for uncertain continuous singular systems with time‐delay. First, on the basis of the Lyapunov functional method and by resorting to the delay‐partition technique, improved delay‐dependent sufficient conditions are presented to ensure the nominal unforced system to be admissible (i.e., to be regular, impulse‐free, and stable). Second, with the help of the obtained admissibility criterion, an observer‐based controller is designed by solving a set of LMIs. Finally, the validity and applicability of the proposed approach is shown by examples. Copyright © 2013 John Wiley & Sons, Ltd.     

Delay‐dependent filtering design for time‐delay systems with Markovian jumping parameters

Two filtering problems—H_∞ filtering and H₂ filtering—for the linear Markovian jump systems with time delay are considered in this paper. The proposed new filtering approach guarantees that the results are less conservative than that obtained by other existing approaches. Numerical example well demonstrates the proposed algorithms. Copyright © 2006 John Wiley & Sons, Ltd.     

Observer design for nonlinear parameter‐varying systems: Application to diesel engines

This paper deals with the problem of designing a nonlinear observer for diesel engines. The goal is to estimate the masses entering the cylinders and the inlet and exhaust pressures. To achieve this, the considered model subject to disturbances contains linear parameter‐varying part and nonlinear part having a large Lipschitz constant. The H _∞ criterion is used to reject the disturbances. Besides, the modified mean value theorem is applied to express the nonlinear error dynamics as a convex combination of known matrices with time‐varying coefficients. The sufficient conditions are derived and given in terms of linear matrix inequality. The advantage of the proposed method is that it can be applied to a wider class of nonlinear systems, particulary our case: diesel engines. The proposed approach is tested and evaluated using an advanced diesel engine professional simulator AMEsim (LMS International, Leuven, Belgium). Copyright © 2014 John Wiley & Sons, Ltd.