H 2 , H ∞ , and mixed H 2 /H ∞ FIR Filters for Discrete-time State Space Models

In this paper a new type of filter, called the H₂ / H ∞ , FIR filter, is proposed for discrete-time state space signal models. The proposed filter requires linearity, unbiased property, FIR structure, and independence of the initial state information in addition to the performance criteria in both H₂ and H ∞ , sense. It is shown that H₂, H ∞ , and H₂/ H ∞ FIR filter design problems can be converted into convex programming problems via linear matrix inequalities (LMIs) with a linear equality constraint. Simulation studies illustrate that the proposed FIR filter is more robust against temporary uncertainties and has faster convergence than the conventional IIR filters.

[1]  Hee-Seob Ryu,et al.  Robust H∞ Fir Filter for Uncertain Systems , 1996 .

[2]  Maria Elena Valcher.  State observers for discrete-time linear systems with unknown inputs , 1999, IEEE Trans. Autom. Control..

[3]  Jae Weon Choi,et al.  Continuous-time deadbeat fault detection and isolation filter design , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[4]  P. Khargonekar,et al.  Filtering and smoothing in an H/sup infinity / setting , 1991 .

[5]  Wook Hyun Kwon,et al.  A receding horizon Kalman FIR filter for linear continuous-time systems , 1999, IEEE Trans. Autom. Control..

[6]  Wook Hyun Kwon,et al.  A receding horizon unbiased FIR filter for discrete-time state space models , 2002, Autom..

[7]  Maurício C. de Oliveira,et al.  H2 and H∞ robust filtering for convex bounded uncertain systems , 2001, IEEE Trans. Autom. Control..

[8]  D. McFarlane,et al.  Optimal guaranteed cost control and filtering for uncertain linear systems , 1994, IEEE Trans. Autom. Control..

[9]  Uri Shaked,et al.  Robust minimum variance filtering , 1995, IEEE Trans. Signal Process..

[10]  Wook Hyun Kwon,et al.  Receding-horizon unbiased FIR filters for continuous-time state-space models without a priori initial state information , 2001, IEEE Trans. Autom. Control..

[11]  Minyue Fu,et al.  A linear matrix inequality approach to robust H∞ filtering , 1997, IEEE Trans. Signal Process..

[12]  Hee-Seob Ryu,et al.  Robust H/sub /spl infin// FIR filter for discrete-time uncertain systems , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[13]  Lihua Xie,et al.  H∞ estimation for uncertain systems , 1992 .

[14]  J.C. Geromel,et al.  H/sub 2/ and H/sub /spl infin// robust filtering for convex bounded uncertain systems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[15]  Wook Hyun Kwon,et al.  A receding horizon Kalman FIR filter for discrete time-invariant systems , 1999, IEEE Trans. Autom. Control..

[16]  P. Khargonekar,et al.  Filtering and smoothing in an H/sup infinity / setting , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[17]  Lihua Xie,et al.  Robust Kalman filtering for uncertain discrete-time systems , 1994, IEEE Trans. Autom. Control..

[18]  Lihua Xie,et al.  H∞ estimation for discrete-time linear uncertain systems , 1991 .