Two algorithms for fast and accurate passivity-preserving model order reduction

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

Volumn 25, Issue 10, 2006, Pages 2062-2074

  Wong, Ngai ^a,b   Balakrishnan, Venkataramanan ^a,c   Koh, Cheng Kok ^a,c   Ng, Tung Sang ^a,b  

^a IEEE   (Hong Kong)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

^c PURDUE UNIVERSITY   (United States)

Author keywords

Algebraic riccati equation; Balanced stochastic truncation (BST); Newton method; Smith method; SR algorithm

Indexed keywords

ALGEBRAIC RICCATI EQUATION; BALANCED STOCHASTIC TRUNCATION (BST); NEWTON METHOD; SMITH METHOD; SR ALGORITHM;

ALGORITHMS; COMPUTATIONAL METHODS; COMPUTER SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; HAMILTONIANS; MATHEMATICAL MODELS; PROBLEM SOLVING;

RICCATI EQUATIONS;

EID: 33748288305     PISSN: 02780070     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCAD.2006.873893     Document Type: Article

References (33)

1. A. Odabasioglu, M. Celik, and L. T. Pileggi, "PRIMA: Passive reducedorder interconnect macromodeling algorithm," IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., vol. 17, no. 8, pp. 645-654, Aug. 1998.
2. Z. Bai, P. M. Dewilde, and R. W. Freund, Reduced-Order Modeling, Mar. 2002, Murray Hill, NJ: Bell Laboratories. Numerical Analysis Manuscript 02-4-13.
3. L. T. Pillage and R. A. Rohrer, "Asymptotic waveform evaluation for timing analysis," IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., vol. 9, no. 4, pp. 352-366, Apr. 1990.
4. P. Feldmann and R. W. Freund, "Efficient linear circuit analysis by Padé approximation via the Lanczos process," IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., vol. 14, no. 5, pp. 639-649, May 1995.
5. _, "Reduced-order modeling of large linear subcircuits via a block Lanczos algorithm," in Proc. ACM/IEEE Des. Autom. Conf., Jun. 1995, pp. 474-479.
6. ∞ -error bounds," Int. J. Contr., vol. 39, no. 6, pp. 1115-1193, Jun. 1984.
7. B. Moore, "Principal component analysis in linear systems: Controllability, observability, and model reduction," IEEE Trans. Automat. Contr., vol. AC-26, no. 1, pp. 17-32, Feb. 1981.
8. T. Penzl, "Algorithms for model reduction of large dynamical systems," FRG, Chemnitz, Germany, Tech. Rep. SFB393/99-40, 1999. Sonder-forschungsbereich 393 Numerische Simulation auf massiv parallelen Rechnern, TU Chemnitz.
9. Q. Su, "Algorithms for model reduction of large scale RLC systems," Ph.D. dissertation, School ECE, Purdue Univ., Lafayette, IN, Aug. 2002.
10. M. Green, "Balanced stochastic realizations," Linear Algebra Appl., vol. 98, pp. 211-247, Jan. 1988.
11. X. Chen and J. T. Wen, "Positive realness preserving model reduction with Haa norm error bounds," IEEE Trans. Circuits Syst. I, Fundam, Theory Applicat., vol. 42, no. 1, pp. 23-29, Jan. 1995.
12. J. R. Phillips, L. Daniel, and L. M. Silveira, "Guaranteed passive balancing transformations for model order reduction," IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., vol. 22, no. 8, pp. 1027-1041, Aug. 2003.
13. Q. Su, V. Balakrishnan, and C.-K. Koh, "Efficient approximate balanced truncation of general large-scale RLC systems via Krylov methods," in Proc. ASPDAC/Int. Conf. VLSI Des., Jan. 2002, pp. 311-316.
14. _, "A factorization-based framework for passivity-preserving model reduction of RLC systems," in Proc. IEEE Design Automation Conf., Jun. 2002, pp. 40-45.
15. J. Li and J. White, "Efficient model reduction of interconnect via approximate system Gramians," in Proc. IEEE Int. Conf. Comput.-Aided Des., Nov. 1999, pp. 380-383.
16. T. Penzl, "A cyclic low rank Smith method for large sparse Lyapunov equations with applications in model reduction and optimal control," SIAMJ. Sei. Comput., vol. 21, no. 4, pp. 1401-1418, 2000.
17. J. Li, "Model reduction of large linear systems via low rank system Gramians," Ph.D. dissertation, Dept. Math., MIT, Cambridge, MA, Sep. 2000.
18. N. Wong, V. Balakrishnan, C.-K. Koh, and T. S. Ng, "A fast Newton/Smith algorithm for solving algebraic Riccati equations and its application in model order reduction," in Proc. IEEE Conf. Acoust., Speech, Signal Process., May 2004, pp. 53-56.
19. N. Wong, V. Balakrishnan, and C.-K. Koh, "Passivity-preserving model reduction via a computationally efficient project-and-balance scheme," in Proc. IEEE Design Automation Conf., Jun. 2004, pp. 369-374.
20. S. Gugercin and A. C. Antoulas, "A survey of model reduction by balanced truncation and some new results," Int. J. Contr., vol. 77, no. 8, pp. 748-766, 2004.
21. G. Golub and C. V. Loan, Matrix Computations, 2nd ed. Baltimore, MD: Johns Hopkins Univ. Press, 1989.
22. V. Mehrmann, The Autonomous Linear Quadratic Control Problem: Theory and Numerical Solution, ser. 163 Lecture Notes in Control and Information Sciences. Berlin, Germany: Springer-Verlag, Nov. 1991.
23. J. Li and J. White, "Low-rank solution of Lyapunov equations," SIAM Rev., vol. 46, no. 4, pp. 693-713, 2004.
24. A. S. Hodel and K. R. Poolla, "Heuristic approaches to the solution of very large sparse Lyapunov and algebraic Riccati equations," in Proc. Conf. Decision Control, Dec. 1988, pp. 2217-2221.
25. G. S. Ammar, P. Benner, and V. Mehrmann, "A multishift algorithm for the numerical solution of algebraic Riccati equations," Electron. Trans. Numer. Anal., vol. 1, pp. 33-48, Sep. 1993.
26. P. Benner, V. Mehrmann, and H. Xu, "A new method for computing the stable invariant subspace of a real Hamiltonian matrix," J. Comput. Appl. Math., vol. 86, no. 1, pp. 17-43, Nov. 1997.
27. P. Benner, V. Mehrmann, V. Sima, S. Van-Huffel, and A. Varga, "SLICOT - A subroutine library in systems and control theory," in Applied and Computational Control, Signals and Circuits, vol. 1, B. N. Datta, Ed. Boston, MA: Birkauser, 1999, ch. 10, pp. 499-539.
28. P. Benner and R. Byers, "An exact line search method for solving generalized continuous-time algebraic Riccati equations," IEEE Trans. Automat. Contr., vol. 43, no. 1, pp. 101-107, Jan. 1998.
29. J. Vlach and K. Singhal, Computer Methods for Circuit Analysis and Design. Norwell, MA: Kluwer, Jul. 1993.
30. H. Weiss, Q. Wang, and J. L. Speyer, "System characterization of positive real conditions," IEEE Trans. Automat. Contr., vol. 39, no. 3, pp. 540-544, Mar. 1994.
31. P. Benner and H. Faßbender, "An implicitly restarted symplectic Lanczos method for the Hamiltonian eigenvalue problem," Linear Algebra Appl., vol. 263, no. 1-3, pp. 75-111, Sep. 1997.
32. P.-A. Absil, R. Mahony, and R. Sepulchre, "Riemannian geometry of Grassmann manifolds with a view on algorithmic computation," Acta Appl. Math., vol. 80, no. 2, pp. 199-220, Jan. 2004.
33. A. Bunse-Gerstner and V. Mehrmann, "A symplectic QR like algorithm for the solution of the real algebraic Riccati equation," IEEE Trans. Automat. Contr., vol. AC-31, no. 12, pp. 1104-1113, Dec. 1986.