A simple design method of reduced-order filters and its applications to multirate filter bank design

Based on linear matrix inequality (LMI) technique, a new design method is proposed for the reduced-order filters of continuous and discrete time 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 proposed method can be used to design H"2 and H"~ reduced-order filters and multirate filter banks. Its effectiveness is illustrated by several examples.

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

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

[3]  K. Glover,et al.  Controller approximation: approaches for preserving H-infinity performance , 1998 .

[4]  B. Francis,et al.  Input-output gains of linear periodic discrete-time systems with application to multirate signal processing , 1996, 1996 IEEE International Symposium on Circuits and Systems. Circuits and Systems Connecting the World. ISCAS 96.

[5]  Tongwen Chen,et al.  Design of multirate filter banks by /spl Hscr//sub /spl infin// optimization , 1995 .

[6]  K. Grigoriadis,et al.  Reduced-order H/sub /spl infin// and L/sub 2/-L/sub /spl infin// filtering via linear matrix inequalities , 1997, IEEE Transactions on Aerospace and Electronic Systems.

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

[8]  Tomomichi Hagiwara,et al.  On H-infinity model reduction using LMIs , 2004 .

[9]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[10]  David Zhang,et al.  Improved robust H2 and Hinfinity filtering for uncertain discrete-time systems , 2004, Autom..

[11]  Victor Sreeram,et al.  Balanced performance preserving controller reduction , 2002, Syst. Control. Lett..

[12]  Ravi N. Banavar,et al.  A mixed norm performance measure for the design of multirate filterbanks , 2001, IEEE Trans. Signal Process..

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

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

[15]  Tongwen Chen,et al.  Design of multirate filter banks by 𝒽∞ optimization , 1995, IEEE Trans. Signal Process..

[16]  P. Vaidyanathan.  Multirate Systems And Filter Banks , 1992 .

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

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

[19]  Wei-Yong Yan,et al.  Parametrization and optimization of reduced-order filters , 1999, IEEE Trans. Autom. Control..

[20]  Jian Huang,et al.  A direct approach to the design of QMF banks via frequency domain optimization , 1998, IEEE Trans. Signal Process..

[21]  Jingxin Zhang,et al.  H2/H, Signal Reconstruction in Noisy Filter Bank Systems , 2000 .

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

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

[24]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .