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.

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
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