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Optimal fault detection for linear discrete time-varying systems. (English) Zbl 1204.93078
Summary: This paper deals with the problem of observer-based fault detection for Linear Discrete Time-Varying (LDTV) systems. A problem formulation is first proposed to address the optimization of the Fault Detection Filter (FDF) design, which is expressed in terms of maximizing a finite horizon $H_\infty/H_\infty$ or $H_-/H_\infty$ performance index. This formulation can be applied to FDF design of LDTV systems subject to $l_{2}$-norm bounded unknown inputs or stochastic noise sequences. It is shown that a unified optimal solution to the FDF can be obtained by solving the discrete time Riccati equation and the optimal FDF is not unique. A numerical example is given to illustrate the proposed method.

93C55Discrete-time control systems
93C05Linear control systems
93D05Lyapunov and other classical stabilities of control systems
Full Text: DOI
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