A simple design method of Hinfinity reduced-order filters for stochastic systems

This paper is concerned with reduced-order /sub /spl infin// filtering of stochastic systems. Based on linear matrix inequality (LMI) technique, a new design method is proposed for the reduced-order filtering of stochastic linear systems. The method is derived from decomposing the key matrix in LMIs which determines the order of designed filters. Different from the existing methods, the proposed method first minimizes the upper bound of the key matrix and then eliminates its near-zero eigenvalues, which results in a simpler, more direct and reliable design procedure. The method is applicable to both continuous and discrete time stochastic systems. Its effectiveness is illustrated by an example.

[1]  D. Hinrichsen,et al.  H∞-type control for discrete-time stochastic systems , 1999 .

[2]  J. Geromel,et al.  A new discrete-time robust stability condition , 1999 .

[3]  D. Hinrichsen,et al.  Stochastic $H^\infty$ , 1998 .

[4]  Shengyuan Xu,et al.  Reduced-order H∞ filtering for stochastic systems , 2002, IEEE Trans. Signal Process..

[5]  P. Apkarian,et al.  Fixed‐order H∞ control design via a partially augmented Lagrangian method , 2003 .

[6]  Maurício C. de Oliveira,et al.  H[sub 2] and Hinfinity Robust Filtering for Discrete-Time Linear Systems , 2000, SIAM J. Control. Optim..

[7]  Lin Huang,et al.  Controller order reduction with guaranteed performance via coprime factorization , 2003 .

[8]  Tomomichi Hagiwara,et al.  On H/sub /spl infin// model reduction using LMIs , 2004 .

[9]  P. Gahinet,et al.  A linear matrix inequality approach to H∞ control , 1994 .

[10]  Truong Q. Nguyen,et al.  Robust mixed 𝒽2/𝒽∞ filtering of 2-D systems , 2002, IEEE Trans. Signal Process..

[11]  J. Geromel,et al.  Extended H 2 and H norm characterizations and controller parametrizations for discrete-time systems , 2002 .

[12]  Pierre Apkarian,et al.  Robust mixed /spl Hscr//sub 2///spl Hscr//sub /spl infin// filtering of 2-D systems , 2002 .

[13]  Wei-Yong Yan,et al.  L2 optimal filter reduction: a closed-loop approach , 1998, IEEE Trans. Signal Process..

[14]  Isaac Yaesh,et al.  Hinfinity control and filtering of discrete-time stochastic systems with multiplicative noise , 2001, Autom..

[15]  K. Glover,et al.  Controller approximation: approaches for preserving H∞ performance , 1998, IEEE Trans. Autom. Control..

[16]  Truong Q. Nguyen,et al.  Robust and reduced-order filtering: new LMI-based characterizations and methods , 2001, IEEE Trans. Signal Process..

[17]  Tomomichi Hagiwara,et al.  On H∞ model reduction using LMIs , 2004, IEEE Trans. Autom. Control..