Relative-error bound for discrete balanced stochastic truncation

REFERENCES

• AL-SAGGAF , U. M. , and FRANKLIN , G. F. , 1987 , An error bound for a discrete reduced order model of a linear multivariate system . I.E.E.E. Transactions on Automatic Control , 32 , 815 – 819 ; 1988, Model reduction via balanced realizations an extension and frequency weighting techniques. Ibid., 33, 687–692 .
   Web of Science ®Google Scholar
• ANDERSON , B. D. O. , and VONGPANITLERD , S. , 1973 , Network Analysis and Synthesis, a Modern Systems Theory Approach ( Englewood Cliffs , NJ Prentice Hall ).
   Google Scholar
• DESAI , U. B. , and PAL , D. , 1984 , A transformation approach to stochastic model reduction . I.E.E.E. Transactions on Automatic Control , 29 , 1097 – 1100 .
   Web of Science ®Google Scholar
• GLOVER , K. 1986 , Multiplicative approximation of linear multivariable systems with L∞ error bounds . Proceedings of the American Control Conference , Seattle, Washington , pp. 1705 – 1709 .
   Google Scholar
• GLOVER , K. , and JONCKHEERE , E. , 1986 , A comparison of two Hankel-norm methods for approximating spectra . Modelling, Identification and Robust Control , edited by C. I. Byrnes and A. Lindquist ( Amsterdam North-Holland ), pp. 297 – 306 .
   Google Scholar
• GREEN , M. , 1988 a , Balanced stochastic realization . Journal of Linear Algebra and Its Applications , 98 , 211 – 247 ; 1988 b, A relative error bound for balanced stochastic truncation. I.E.E.E. Transactions on Automatic Control, 33, 961–965 .
   Web of Science ®Google Scholar
• GREEN , M. , and ANDERSON , B. D. O. , 1989 , Model reduction by phase matching , Mathematics of Control, Signals and Systems , 2 , 221 – 263 .
   Google Scholar
• HARSHAVARDHANA , P. , JONCKHEERE , E. A. , and SILVERMAN , L. M. , 1984 , Stochastic balancing and approximation—stability and minimality . I.E.E.E. Transactions on Automatic Control , 29 , 744 – 746 .
   Web of Science ®Google Scholar
• HINRICHSEN , D. , and PRITCHARD , A. J. , 1990 , An improved error estimate for reduced-order models of discrete-time systems . I.E.E.E. Transactions on Automatic Control , 35 , 317 – 320 .
   Web of Science ®Google Scholar
• KAILATH , T. , 1980 , Linear Systems ( Englewood Cliffs , NJ Prentice Hall ).
   Google Scholar
• Liu , Y. , and ANDERSON , B. D. O. , 1989 , Singular perturbation approximation of balanced systems . International Journal of Control , 50 , 1379 – 1405 .
   Web of Science ®Google Scholar
• MOORE , B. C. , 1981 , Principle component analysis in linear systems controllability, observability and model reduction . I.E.E.E. Transactions on Automatic Control , 26 , 17 – 32 .
   Web of Science ®Google Scholar
• OPDENACKER , Ph. C. , and JONCKHEERE , E. A. , 1986 , A state space approach to approximation by phase matching . Modelling, Identification and Robust Control , edited by C. I. Byrnes and A. Lindquist ( Amsterdam North-Holland ), pp. 249 – 362 .
   Google Scholar
• SAFONOV , M. G. , and CHIANG , R. Y. , 1988 , Model reduction for robust control a Schur relative error method . International Journal of Adaptive Control and Signal Processing , 2 , 259 – 272 .
   Google Scholar
• WANG , W. , 1990 , Relative-error model reduction, identification, and control . Ph.D. thesis , Department of Electrical Engineering-Systems, University of Southern California .
   Google Scholar
• WANG , W. , and SAFONOV , M. G. , 1990 , A tighter relative error bound for balanced stochastic truncation . Systems and Control Letters , 14 , 307 – 317 .
   Web of Science ®Google Scholar