Optimal fault detection for linear discrete time-varying systems. (English) Zbl 1204.93078

Zhong, Maiying; Ding, Steven X.; Ding, Eve L.

Automatica 46, No. 8, 1395-1400 (2010).

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.

MSC:

93C55	Discrete-time control/observation systems
93C05	Linear systems in control theory
93D05	Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory

Keywords:

linear discrete time-varying system; fault detection; observer; post-filter; Riccati equation

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