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.     

Fault detection for discrete‐time switched singular time‐delay systems: an average dwell time approach

In this paper, the fault detection problem is investigated for a class of discrete‐time switched singular systems with time‐varying state delays. The residual generator is firstly constructed based on a switched filter, and the design of fault detection filter is formulated as an H _∞ filtering problem, that is, minimizing the error between residual and fault in the H _∞ sense. Then, by constructing an appropriate decay‐rate‐dependent piecewise Lyapunov function and using the average dwell time scheme, a sufficient condition for the residual system to be regular, causal, and exponential stable while satisfying a prescribed H _∞ performance is derived in terms of linear matrix inequalities (LMIs). The corresponding solvability condition for the desired fault detection filters is also established via LMI approach. Finally, a numerical example is presented to show the effectiveness of the developed theoretical results.Copyright © 2012 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.     

Stability and stabilization in switched discrete‐time systems

In this paper, we investigate the stability and stabilization problem for discrete‐time switched systems. We consider a probabilistic case where the system is switched among different subsystems, and the probability of each subsystem being active is defined as its occurrence probability. The relationship between the developed model of the switched system and the Markovian jump system is analyzed. For a switched system with a known subsystem occurrence probabilities, we give a stochastic stability criterion in terms of a linear matrix inequality. Then, we extend the results to a more practical case where the subsystem occurrence probabilities of switching are known to be constant, but their specific values are only known with some uncertainty. A new iterative approach is employed to choose the switching law between the subsystems. For unstable switched systems, mode‐dependent state feedback and static output feedback controllers are developed to achieve the stabilization objective. Finally, several simulation examples are presented to show the efficacy of the proposed criteria and methods. Copyright © 2012 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.     

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.     

Constructive approximation of non‐linear discrete‐time systems

It is known that large classes of approximately‐finite‐memory maps can be uniformly approximated arbitrarily well by the maps of certain non‐linear structures. As an application, it was proved that time‐delay networks can be used to uniformly approximate arbitrarily well the members of a large class of causal nonlinear dynamic discrete‐time input–output maps. However, the proof is non‐constructive and provides no information concerning the determination of a structure that corresponds to a prescribed bound on the approximation error. Here we give some general results concerning the problem of finding the structure. Our setting is as follows. There is a large family 𝒢 of causal time‐invariant approximately‐finite‐memory input‐output maps G from a set S of real d‐vector‐valued discrete‐time inputs (with d⩾1) to the set of ℝ‐valued discrete‐time outputs, with both the inputs and outputs defined on the non‐negative integers 𝒵₊. We show that for each ϵ>0, any Gϵ𝒢 can be uniformly approximated by a structure map H(G, ·) to within tolerance ϵ, and we give analytical results and an example to illustrate how such a H(G, ·) can be determined in principle. Copyright © 2000 John Wiley & Sons, Ltd.     

Robust fault-tolerant control for discrete-time switched systems with time delays

This study outlines the problem of active fault-tolerant control for delayed discrete-time switched systems. Using switched proportional-integral observer and multiple Lyapunov-Krasovski function, less conservative sufficient conditions are established to design a robust fault estimation (FE) algorithm via linear matrix inequality form. Afterward, a fault-tolerant performance is realized based on this fast and exact FE information to compensate the effect of actuator fault while stabilizing the closed-loop system. The efficiency of the proposed strategy is proved through simulation examples and comparison results.     

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.     

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.     

Threshold computation for fault detection in linear discrete‐time Markov jump systems

This paper proposes a threshold computation scheme for an observer‐based fault detection (FD) in linear discrete‐time Markovian jump systems. An observer‐based FD scheme typically consists of two stages known as residual generation and residual evaluation. Even information of faults is contained inside a residual signal, a decision of faults occurrence is consequently made by a residual evaluation stage, which consists of residual evaluation function and threshold setting. For this reason, a successful FD strongly depends on a threshold setting for a given residual evaluation function. In this paper, Kalman filter (KF) is used as a residual generator. Based on an accessibility of Markov chain to KF, two types of residual generations are considered, namely mode‐dependent and mode‐independent residual generation. After that threshold is computed in a residual evaluation stage such that a maximum fault detection rate is achieved, for a given false alarm rate. Without any knowledge of a probability density function of residual signal before and after fault occurrence, a threshold is computed by using an estimation of residual evaluation function variance in a fault‐free case. Finally, a detection performance is demonstrated by a numerical example. Copyright © 2013 John Wiley & Sons, Ltd.     

State estimation for short‐time switched linear systems under asynchronous switching

In this note, the state estimation problem for a class of short‐time switched linear systems is investigated. By incorporating the concept of finite‐time stability, an observer is designed to ensure the error dynamics finite‐time stable in the short‐time switching interval under the general asynchronous switching whereas synchronous switching mode is its special case. A numerical example is provided to illustrate the effectiveness of our study in this paper. Copyright © 2013 John Wiley & Sons, Ltd.     

Quasi‐passivity‐based adaptive stabilization for switched nonlinearly parameterized systems

This paper investigates the adaptive quasi‐passification‐based stabilization problem for a class of switched nonlinearly parameterized systems via average dwell time method. First, when all the subsystems have any same relative degree, the global practical stability is achieved by combining the recursive feedback quasi‐passification design technique with a switched adaptive control technique. The states and parameter estimation errors converge to the ball whose sizes can be reduced by choosing appropriate design parameters. Second, when the system states are unavailable for measurements, adaptive output feedback controllers are designed to stabilize the system using quasi‐passivity. The proposed output feedback controllers do not depend on any state observer. Finally, three examples show the effectiveness of the proposed methods.     

LMI solutions to the mixed ℋ︁−/ℋ︁∞ fault detection observer design for linear parameter‐varying systems

This paper addresses the mixed ??_?/??_∞ fault detection observer design issue for a class of linear parameter‐varying (LPV) systems. Analogous to the definition of the quadratic ??_∞ performance for LPV systems and the ??_? index for linear time invariant (LTI) systems, the quadratic ??_? index and the affine quadratic ??_? index for LPV systems are defined in terms of linear matrix inequalities (LMIs). The first algorithm for designing the mixed ??_?/H_∞ observer is proposed, which aims at minimizing the quadratic ??_∞ performance and maximizing the quadratic ??_? index of the observer error dynamic systems. To reduce the conservativeness of this algorithm, the affine quadratic ??_∞ performance and the affine ??_? index for LPV systems are utilized. The robustness conditions and affine ??_? index conditions for the underlying observer optimization issue are formulated as parameter‐dependent LMIs. The Gridding technique and multi‐convexity concept are applied, respectively, for reducing the parameter‐dependent LMIs to finite LMI constraints. Correspondingly, two iterative algorithms are proposed. Furthermore, the threshold design and the estimation of the worst undetectable fault size are investigated. An example is studied to demonstrate the effectiveness of the proposed algorithms. Copyright © 2010 John Wiley & Sons, Ltd.     

Integrated design of fault detection,isolation, and control for continuous‐time Markovian jump systems

In this paper, the problem of integrated fault detection, isolation, and control design of continuous‐time Markovian jump linear systems with uncertain transition probabilities is introduced and addressed for the first time in the literature. A single Markovian jump module designated as the integrated fault detection, isolation, and control under a mixed robust framework is considered to simultaneously achieve the desired detection, isolation, and control objectives. Conventional mixed robust approaches to the fault detection and isolation problem lead to conservative results due to the selection of identical Lyapunov matrices. Consequently, the extended linear matrix inequality methodology is utilized in this work to reduce the conservativeness of standard approaches by introducing additional matrix variables so that the coupling of Lyapunov matrices with the system matrices is eliminated. Simulation results for an application to the GE F‐404 aircraft engine system illustrate the effectiveness and capabilities of our proposed design methodologies. Comparisons with relevant work in the literature are also provided to demonstrate the advantages of our proposed solutions.     

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.     

Finite‐time dissipativity‐based filter design for networked control systems

This paper investigates the problem of finite‐time boundedness and dissipativity‐based filter design for networked control systems together with parameter uncertainties and random packet dropouts. The packet transmission information is defined by using Bernoulli distributed white sequence which characterizes the measurement conditions. Some new sufficient conditions are established to ensure that the filtering error system is stochastically finite‐time bounded and strictly finite‐time dissipative. These sufficient conditions to design the filter parameters are derived by using linear matrix inequalities and reciprocally convex approach. Finally, an example is given to validate the effectiveness of the proposed filter design.     

A finite frequency approach to filter design for uncertain discrete‐time systems

This paper studies the problem of finite frequency filter design for linear time‐invariant discrete‐time systems with polytopic uncertainties. Generalized Kalman–Yakubovich–Popov lemma is exploited to formulate the filter design problem in finite frequency domain. A design method is presented in terms of solutions to a set of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.