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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.

MSC:
 93C55 Discrete-time control systems 93C05 Linear control systems 93D05 Lyapunov and other classical stabilities of control systems
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References:
 [1] Anderson, B. D. O.; Moore, J. B.: Detectability and stabilizability of time-varying discrete-time linear systems, SIAM journal on control and optimization 19, 20-32 (1981) · Zbl 0468.93051 · doi:10.1137/0319002 [2] Casavola, A.; Famularo, D.; Franze, G.: Robust fault detection of uncertain linear systems via quasi-lmis, Automatica 44, 289-295 (2008) · Zbl 1138.93417 · doi:10.1016/j.automatica.2007.05.010 [3] Chen, J.; Patton, R. J.: Robust model-based fault diagnosis for dynamic systems, (1999) · Zbl 0920.93001 [4] Ding, S. X.: Model-based fault diagnosis techniques, (2008) [5] Ding, S. X.; Jeinsch, T.; Frank, P. M.; Ding, E. L.: A unified approach to the optimization of fault detection systems, International journal of adaptive control and signal processing 14, 725-745 (2000) · Zbl 0983.93016 · doi:10.1002/1099-1115(200011)14:7<725::AID-ACS618>3.0.CO;2-Q [6] Ding, S. X., Zhong, M., & Tang, B. (2001). An LMI approach to the design of fault detection filter for time-delay LTI systems with unknown inputs. In Proc. Amer. contr. conf. Arlington, VA (pp. 2137-2142). [7] Frank, P. M.; Ding, X.: Survey of robust residual generation and evaluation methods in observer-based fault detection systems, Journal of process control 7, 403-424 (1997) [8] Gertler, J.: Fault detection and diagnosis in engineering systems, (1998) [9] Henry, D.; Zolghadri, A.: Norm-based design of robust FDI schemes for uncertain systems under feedback control: comparison of two approaches, Control engineering practice 14, 1081-1097 (2006) [10] Izadi, I.; Zhao, Q.; Chen, T.: Analysis of performance criteria in sampled-data fault detection, Systems & control letters 56, 320-325 (2007) · Zbl 1112.93048 · doi:10.1016/j.sysconle.2006.10.019 [11] Li, X. (2009). Fault detection filter design for linear systems. In Ph.D. dissertation. Louisiana State University, USA, (pp. 66-82). [12] Liu, N., & Zhou, K. (2007). Optimal robust fault detection for linear discrete time systems. In Proc. 46th IEEE conf. decis. contr. New Orleans, USA (pp. 989-994). [13] Li, X.; Zhou, K.: A time domain approach to robust fault detection of linear time-varying systems, Automatica 45, 94-102 (2009) · Zbl 1154.93341 · doi:10.1016/j.automatica.2008.07.017 [14] Wang, J.; Yang, G.; Liu, J.: An LMI approach to H- index and mixed H-/H$\infty$fault detection observer design, Automatica 43, 1656-1665 (2007) · Zbl 1128.93321 · doi:10.1016/j.automatica.2007.02.019 [15] Zhang, P.; Ding, S. X.: Observer-based fault detection of linear time-varying systems, Automatisierungstechnik 52, 370-376 (2004) [16] Zhang, P.; Ding, S. X.; Wang, G.; Zhou, D.: Fault detection of linear discrete-time periodic systems, IEEE transactions on automatic control 50, 239-244 (2005) [17] Zhang, P.; Ding, S. X.; Wang, G.; Zhou, D.: Disturbance decoupling in fault detection of linear periodic systems, Automatica 43, 1410-1417 (2007) · Zbl 1130.93377 · doi:10.1016/j.automatica.2007.01.005 [18] Zhong, M.; Ding, S. X.; Lam, J.; Wang, H.: LMI approach to design robust fault detection filter for uncertain LTI systems, Automatica 39, 543-550 (2003) · Zbl 1036.93061 · doi:10.1016/S0005-1098(02)00269-8 [19] Zhong, M.; Liu, S.; Zhao, H.: Krein space-based H$\infty$fault estimation for linear discrete time-varying systems, ACTA automatica sinica 34, 1529-1533 (2008) · Zbl 1199.93189 · doi:10.3724/SP.J.1004.2008.01529