Robust synchronization and fault detection of uncertain master-slave systems with mixed time-varying delays and nonlinear perturbations

Karimi, Hamid Reza; Luo, Na

doi:10.1109/systol.2010.5675956

Cited by 15 publications

(23 citation statements)

References 45 publications

(49 reference statements)

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“…For probability 1, our results reduce to those for the traditional deterministic fault estimation problem and, in the case of probability 0, the fault estimation problem is no longer valid and our developed approach applies to the state estimation problem only. In the case that all the time-varying parameters become time-invariant (constant), (13)- (14) would become a rather standard Riccati difference equation whose feasibility has been widely investigated in the literature, see e.g. [32].…”

Section: Problem Formulationmentioning

confidence: 99%

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Finite-horizon estimation of randomly occurring faults for a class of nonlinear time-varying systems

et al. 2014

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This paper is concerned with the finite-horizon estimation problem of randomly occurring faults for a class of nonlinear systems whose parameters are all time-varying. The faults are assumed to occur in a random way governed by two sets of Bernoulli distributed white sequences. The stochastic nonlinearities entering the system are described by statistical means that can cover several classes of well-studied nonlinearities. The aim of the problem is to estimate the random faults, over a finite horizon, such that the influence from the exogenous disturbances onto the estimation errors is attenuated at the given level quantified by a H∞-norm in the mean square sense. By using the completing squares method and stochastic analysis techniques, necessary and sufficient conditions are established for the existence of the desired finite-horizon H∞ fault estimator whose parameters are then obtained by solving coupled backward recursive Riccati difference equations (RDEs). A simulation example is utilized to illustrate the effectiveness of the proposed fault estimation method.

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Section: Problem Formulationmentioning

confidence: 99%

“…. , N − 1, assume that the discrete Riccati difference equation (13) has a solution (P (k), F (k), G(k)) satisfying (14) and the following discrete Riccati difference equation:…”

Section: Problem Formulationmentioning

confidence: 99%

Finite-horizon estimation of randomly occurring faults for a class of nonlinear time-varying systems

et al. 2014

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“…Examples include, but are not limited to, stochastic complex networks [20], [36], complex networks with imperfect measurements [33], [35], uncertain complex networks [21], [31] as well as complex networks with various kinds of transmission delays [9], [15]. It is noticeable that, for some complex networks such as power networks and neural networks, the node systems are often subject to singular perturbations.…”

Section: Introductionmentioning

confidence: 99%

An Integrated Approach to Global Synchronization and State Estimation for Nonlinear Singularly Perturbed Complex Networks

Cai

Wang

et al. 2015

IEEE Trans. Cybern.

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Abstract-This paper aims to establish a unified framework to handle both the exponential synchronization and state estimation problems for a class of nonlinear singularly perturbed complex networks (SPCNs). Each node in the SPCN comprises both "slow" and "fast" dynamics that reflects the singular perturbation behavior. General sector-like nonlinear function is employed to describe the nonlinearities existing in the network. All nodes in the SPCN have the same structures and properties. By utilizing a novel Lyapunov functional and the Kronecker product, it is shown that the addressed SPCN is synchronized if certain matrix inequalities are feasible. The state estimation problem is then studied for the same complex network, where the purpose is to design a state estimator to estimate the network states through available output measurements such that dynamics (both "slow" and "fast") of the estimation error is guaranteed to be globally asymptotically stable. Again, a matrix inequality approach is developed for the state estimation problem. Two numerical examples are presented to verify the effectiveness and merits of the proposed synchronization scheme and state estimation formulation. It is worth mentioning that our main results are still valid even if the "slow" subsystems within the network are unstable.

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“…So far, the synchronisation, state estimation and pinning control problems have gained an increasing research interest for various types of complex networks, where the nodes are dynamic systems subject to a variety of engineeringoriented phenomena such as stochastic disturbances [19][20][21], incomplete measurements [22,23], parameter uncertainties [24,25] and mixed (discrete and distributed) time-delays [26,27]. It should be pointed out that, for certain complex networks such as power networks and neural networks, the singular perturbation phenomenon does occur on the corresponding nodes as dynamic systems.…”

Section: Introductionmentioning

confidence: 99%

Decomposition approach to exponential synchronisation for a class of non‐linear singularly perturbed complex networks

Cai

Wang

et al. 2014

IET Control Theory & Applications

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This study is concerned with the globally exponential synchronisation problem for a class of non-linear singularly perturbed complex networks where all nodes possess the same structure and properties. The addressed global synchronisation problem is converted into the one for two lower-order sub-networks, namely, a non-linear slow sub-network and a linear fast sub-network, which are obtained by using the classical singular perturbation decomposition method. The network topology is directed and weighted, which means that the coupling configuration matrix is allowed to be asymmetric. By using the Lyapunov functional method and the Kronecker product technique, sufficient conditions are obtained under which the synchronisation is achieved, respectively, for the two sub-networks and the original complex network. These conditions can be easily verified by using the semi-definite programming method. A numerical example is finally simulated to validate the theoretical results and the effectiveness of the proposed synchronisation scheme.

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Robust synchronization and fault detection of uncertain master-slave systems with mixed time-varying delays and nonlinear perturbations

Cited by 15 publications

References 45 publications

Finite-horizon estimation of randomly occurring faults for a class of nonlinear time-varying systems

Finite-horizon estimation of randomly occurring faults for a class of nonlinear time-varying systems

An Integrated Approach to Global Synchronization and State Estimation for Nonlinear Singularly Perturbed Complex Networks

Decomposition approach to exponential synchronisation for a class of non‐linear singularly perturbed complex networks

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