Balanced Systems and Structures: Reduction, Assignment, and Perturbations

New results on properties of balanced linear systems and structures are presented. Balanced representation is defined for systems with poles at an imaginary axis or at the origin. Grammians do not exist in this case, but antigrammians are introduced which make balanced reduction possible. System grammians of specified properties are obtained by assigning the sensor and actuator configuration. The latter is determined using input-output assignment procedures introduced for general systems and specified to structures. A system is said to be uniformly balanced if all its Hankel singular values are equal.

[1]  New results involving open-loop balanced realization schemes , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[2]  S. Rao,et al.  Model reduction by low frequency approximation of internally balanced representation , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[3]  W. Gawronski,et al.  MODEL REDUCTION FOR SYSTEMS WITH INTEGRATORS , 1992 .

[4]  Fred Y. Hadaegh,et al.  A Hankel singular value approach for identification of low level dynamics in flexible structures , 1990, 29th IEEE Conference on Decision and Control.

[5]  B. Anderson.  A SYSTEM THEORY CRITERION FOR POSITIVE REAL MATRICES , 1967 .

[6]  E. Jonckheere.  Principal component analysis of flexible systems--Open-loop case , 1984 .

[7]  Jer-Nan Juang,et al.  Model reduction for flexible structures , 1990 .

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

[9]  Raymond A. DeCarlo,et al.  Gramian assignment based on the Lyapunov equation , 1990 .

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

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

[12]  A. Laub,et al.  Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms , 1987 .

[13]  S. Weiland.  Balanced representations and approximation of linear systems , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[14]  F. Y. Hadaegh,et al.  Balanced input-output assignment , 1993 .

[15]  Wodek Gawronski,et al.  Model reduction for flexible space structures , 1991 .

[16]  Wodek Gawronski.  Model reduction for flexible structures - Test data approach , 1991 .