Computation of Upper Bounds for the Solution of Continuous Algebraic Riccati Equations

A novel distributed fault detection strategy for a class of nonlinear stochastic systems is presented. Different from the existing design procedures for fault detection, a novel fault detection observer, which consists of a nonlinear fault detection filter and a consensus filter, is proposed to detect the nonlinear stochastic systems faults. Firstly, the outputs of the nonlinear stochastic systems act as inputs of a consensus filter. Secondly, a nonlinear fault detection filter is constructed to provide estimation of unmeasurable system states and residual signals using outputs of the consensus filter. Stability analysis of the consensus filter is rigorously investigated. Meanwhile, the design procedures of the nonlinear fault detection filter are given in terms of linear matrix inequalities (LMIs). Taking the influence of the system stochastic noises into consideration, an outstanding feature of the proposed scheme is that false alarms can be reduced dramatically. Finally, simulation results are provided to show the feasibility and effectiveness of the proposed fault detection approach.

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“…In order to estimate system states, one gives the following full order Luenberger-like observer [13][14][15][16]:…”

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

Distributed Fault Detection for a Class of Nonlinear Stochastic Systems

Yan

Wang

2014

Mathematical Problems in Engineering

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“…Unfortunately, by this time, the upper matrix bounds for the solution of the CARE (4) have not been proposed in the literature. However, Lee in [15] has proposed upper and lower matrix bounds for the CARE (4) and henceforth many reports have been presented for the upper [16][17][18][19][20] and lower [18,19,21] bounds for the solution of the CARE (4). As matrix bounds include all eigenvalue bounds [14,22,23] particularly the minimum and maximum eigenvalues, trace [10,24,25], determinant [14], and norm [26] bounds, it is seen that they are the most general and useful.…”

Section: Introductionmentioning

confidence: 99%

Some Upper Matrix Bounds for the Solution of the Continuous Algebraic Riccati Matrix Equation

Ulukök¹,

Türkmen²

2013

Journal of Applied Mathematics

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We propose diverse upper bounds for the solution matrix of the continuous algebraic Riccati matrix equation (CARE) by building the equivalent form of the CARE and using some matrix inequalities and linear algebraic techniques. Finally, numerical example is given to demonstrate the effectiveness of the obtained results in this work as compared with some existing results in the literature. These new bounds are less restrictive and provide more efficient results in some cases.

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Observer-Based H ∞ Synchronization and Unknown Input Recovery for a Class of Digital Nonlinear Systems

Zhang

Zhu

et al. 2013

Circuits Syst Signal Process

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Computation of Upper Bounds for the Solution of Continuous Algebraic Riccati Equations

Cited by 7 publications

References 27 publications

Distributed Fault Detection for a Class of Nonlinear Stochastic Systems

Distributed Fault Detection for a Class of Nonlinear Stochastic Systems

Some Upper Matrix Bounds for the Solution of the Continuous Algebraic Riccati Matrix Equation

Observer-Based H ∞ Synchronization and Unknown Input Recovery for a Class of Digital Nonlinear Systems

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