DISCRETE SYSTEM ORDER-REDUCTION VIA BALANCING TRANSFORMATION USING SINGULAR PERTURBATIONS

Abstract Order-reduction techniques based on system balancing are developed for linear discrete systems using the method of singular perturbations. The generalized residualization technique is introduced with three variants as improved tools for order-reduction at low and medium frequencies. The newly introduced techniques have the same theoretical upper error bound with respect to the H ∞ norm of the reduced-order system as the existing techniques, but simulation results show the superiority of the new techniques at low and medium frequencies. Next, new techniques are proposed to perform order-reduction of lightly damped linear discrete-time systems by employing the method of singular perturbations and balancing transformation.

[1]  D. Hinrichsen,et al.  An improved error estimate for reduced-order models of discrete-time systems , 1990 .

[2]  Clifford T. Mullis,et al.  Synthesis of minimum roundoff noise fixed point digital filters , 1976 .

[3]  Wodek Gawronski,et al.  Model reduction for flexible space structures , 1989 .

[4]  Vojislav Kecman,et al.  Eigenvector approach for order reduction of singularly perturbed linear-quadratic optimal control problems , 1999, Autom..

[5]  D. Enns.  Model reduction with balanced realizations: An error bound and a frequency weighted generalization , 1984, The 23rd IEEE Conference on Decision and Control.

[6]  Joe H. Chow,et al.  Singular perturbation and iterative separation of time scales , 1979, Autom..

[7]  K. W. Chang.  Singular Perturbations of a General Boundary Value Problem , 1972 .

[8]  Z. Gajic,et al.  The recursive reduced-order numerical solution of the singularly perturbed matrix differential Riccati equation , 1988 .

[9]  C. Gregory.  Reduction of large flexible spacecraft models using internal balancing theory , 1984 .

[10]  K. Fernando,et al.  Singular perturbational approximations for discrete-time balanced systems , 1983 .

[11]  A. Antoulas,et al.  A Survey of Model Reduction by Balanced Truncation and Some New Results , 2004 .

[12]  James Lam,et al.  On the stability of projections of balanced realizations , 1997 .

[13]  Gene F. Franklin,et al.  An error bound for a discrete reduced order model of a linear multivariable system , 1987 .

[14]  Edmond A. Jonckheere,et al.  A new set of invariants for linear systems--Application to reduced order compensator design , 1983 .

[15]  I. Postlethwaite,et al.  Model reduction with balanced realizations , 1995 .

[16]  Zoran Gajic,et al.  Improvement of system order reduction via balancing using the method of singular perturbations , 2001, Autom..

[17]  Victor Sreeram,et al.  Model reduction using balanced realizations with improved low frequency behaviour , 1989 .

[18]  K. Glover.  All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds† , 1984 .

[19]  Desineni S Naidu,et al.  Singular perturbations and time scales in control theory and applications: An overview , 2002 .

[20]  L. Silverman,et al.  Model reduction via balanced state space representations , 1982 .

[21]  B. Moore.  Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .

[22]  Brian D. O. Anderson,et al.  Singular perturbation approximation of balanced systems , 1989 .

[23]  Hassan K. Khalil,et al.  Multirate and composite control of two-time-scale discrete-time systems , 1985 .