Robust reconstruction of the discrete state for a class of nonlinear uncertain switched systems

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Dynamic network model of banking system stability

This paper presents a dynamic model of banking interactions, which uses interbank connections to study the stability of the banking system. The dynamic model extends previous work on network models of the banking system taking inspiration from large scale, complex, interconnected systems studied within the domain of engineering. The banking system is represented as a network where nodes are individual banks and the links between any two banks consist of interbank loans and borrowing. The dynamic structure of the model is represented as a set of differential equations, which, to the best of our knowledge, is an original characteristic of our approach. This dynamic structure not only allows us to analyse systemic risk but also to incorporate an analysis of control mechanisms. Uncertainty is introduced in the system by applying stochastic shocks to the bank deposits, which are assigned as an exogenous signal. The behaviour of the system can be analysed for different initial conditions and parameter sets. This paper shows some preliminary results under different combinations of bank reserve ratios, bank capital sizes and different degrees of bank inter-connectedness. The results show that both reserve ratio and link rate have a positive effect on the stability of the system in the presence of moderate shocks. However, for high values of the shocks, high reserve ratios may have a detrimental effect on the survival of banks. In future work, we will apply strategies from the domain of control engineering to the dynamic model to characterise more formally the stability of the banking network

H∞ fault estimation with randomly occurring uncertainties, quantization effects and successive packet dropouts: The finite-horizon case

In this paper, the finite-horizon H∞ fault estimation problem is investigated for a class of uncertain nonlinear time-varying systems subject to multiple stochastic delays. The randomly occurring uncertainties (ROUs) enter into the system due to the random fluctuations of network conditions. The measured output is quantized by a logarithmic quantizer before being transmitted to the fault estimator. Also, successive packet dropouts (SPDs) happen when the quantized signals are transmitted through an unreliable network medium. Three mutually independent sets of Bernoulli-distributed white sequences are introduced to govern the multiple stochastic delays, ROUs and SPDs. By employing the stochastic analysis approach, some sufficient conditions are established for the desired finite-horizon fault estimator to achieve the specified H∞ performance. The time-varying parameters of the fault estimator are obtained by solving a set of recursive linear matrix inequalities. Finally, an illustrative numerical example is provided to show the effectiveness of the proposed fault estimation approach

On design of quantized fault detection filters with randomly occurring nonlinearities and mixed time-delays

This paper is concerned with the fault detection problem for a class of discrete-time systems with randomly occurring nonlinearities, mixed stochastic time-delays as well as measurement quantizations. The nonlinearities are assumed to occur in a random way. The mixed time-delays comprise both the multiple discrete time-delays and the infinite distributed delays that occur in a random way as well. A sequence of stochastic variables is introduced to govern the random occurrences of the nonlinearities, discrete time-delays and distributed time-delays, where all the stochastic variables are mutually independent but obey the Bernoulli distribution. The main purpose of this paper is to design a fault detection filter such that, in the presence of measurement quantization, the overall fault detection dynamics is exponentially stable in the mean square and, at the same time, the error between the residual signal and the fault signal is made as small as possible. Sufficient conditions are first established via intensive stochastic analysis for the existence of the desired fault detection filters, and then the explicit expression of the desired filter gains is derived by means of the feasibility of certain matrix inequalities. Also, the optimal performance index for the addressed fault detection problem can be obtained by solving an auxiliary convex optimization problem. A practical example is provided to show the usefulness and effectiveness of the proposed design method

H ∞ sliding mode observer design for a class of nonlinear discrete time-delay systems: A delay-fractioning approach

Copyright @ 2012 John Wiley & SonsIn this paper, the H ∞  sliding mode observer (SMO) design problem is investigated for a class of nonlinear discrete time-delay systems. The nonlinear descriptions quantify the maximum possible derivations from a linear model, and the system states are allowed to be immeasurable. Attention is focused on the design of a discrete-time SMO such that the asymptotic stability as well as the H ∞  performance requirement of the error dynamics can be guaranteed in the presence of nonlinearities, time delay and external disturbances. Firstly, a discrete-time discontinuous switched term is proposed to make sure that the reaching condition holds. Then, by constructing a new Lyapunov–Krasovskii functional based on the idea of ‘delay fractioning’ and by introducing some appropriate free-weighting matrices, a sufficient condition is established to guarantee the desired performance of the error dynamics in the specified sliding mode surface by solving a minimization problem. Finally, an illustrative example is given to show the effectiveness of the designed SMO design scheme

Adaptive sliding mode observation in a network of dynamical systems

This paper considers the problem of reconstructing state information in all the nodes of a complex network of dynamical systems. The individual nodes comprise a known linear part and unknown but bounded uncertainties in certain channels of the system. A supervisory adaptive sliding mode observer configuration is proposed for estimating the states. A linear matrix inequality (LMI) approach is suggested to synthesise the gains of the sliding mode observer. Although deployed centrally to estimate all the states of the complex network, the design process depends only on the dynamics of an individual node of the network. The methodology is demonstrated by considering a network of Chua oscillators