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**Observer-based optimal fault detection using pdfs for time-delay stochastic systems.**
*(English)*
Zbl 1156.93395

Summary: This paper concerns the problem of fault detection (FD) for general stochastic systems with time delays. Different from the classical FD problem, the available information for the FD is the input and the measured output probability density functions (PDFs) of the system. Based on this, firstly, square root B-spline expansions technique is applied to model the PDFs so that the concerned FD problem is transformed into a nonlinear FD problem subject to the weight dynamical systems. Secondly, by using the FD observer as residual generator and guaranteed cost performance index as objective function, design of the FD observer is formulated as an optimization problem. A delay-dependent condition to solve this problem is established in terms of the feasibility of linear matrix inequality (LMI). Moreover, in order to improve FD performance, the guaranteed cost algorithm is applied to optimal observer design. Finally, two examples are given to demonstrate the applicability of the proposed approach.

### MSC:

93E10 | Estimation and detection in stochastic control theory |

60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |

34K20 | Stability theory of functional-differential equations |

### Keywords:

fault detection; stochastic system; B-spline expansion; probability density function; delay-dependent; LMI
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\textit{T. Li} et al., Nonlinear Anal., Real World Appl. 9, No. 5, 2337--2349 (2008; Zbl 1156.93395)

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