Balanced reduction of linear periodic systems

Kybernetika

Volumn 35, Issue 6, 1999, Pages 737-751

  Longhi, Sauro ^a   Orlando, Giuseppe ^a  

^a UNIVERSITÀ POLITECNICA DELLE MARCHE   (Italy)

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[No Author keywords available]

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EID: 0033478952     PISSN: 00235954     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (25)

1. U. M. Al-Saggaf and G. F. Franklin: An error bound for a discrete reduced order model of a linear multivariable system. IEEE Trans. Automat. Control AC-32 (1987), 9, 815-819.
2. S. Bittanti: Deterministic and stochastic linear periodic systems. In: Time Series and Linear Systems (S. Bittanti, ed.), Springer-Verlag, Berlin 1986.
3. P. Bolzern and P. Colaneri: Existence and uniqueness conditions for the periodic solutions of the discrete-time periodic Lyapunov equations. In: Proc. of 25th Conference on Decision and Control, Athens 1986, pp. 1439-1443.
4. P. Bolzern, P. Colaneri and R. Scattolini: Zeros of discrete-time linear periodic systems. IEEE Trans. Automat. Control AC-31 (1986), 1057-1059.
5. P. Colaneri and S. Longhi: The lifted and cyclic reformulations in the minimal realization of linear discrete-time periodic systems. In: Proc. of the 1st IFAC Workshop on New Trends in Design of Control Systems, Smolenice 1994, pp. 329-334.
6. P. Colaneri and S. Longhi: The realization problem for linear periodic systems. Automatica 31 (1995), 775-779.
7. D. S. Evans: Finite-dimensional realizations of discrete-time weighting patterns. SIAM J. Appl. Math. 22 (1972), 45-67.
8. D. S. Flamm: A new shift-invariant representation for periodic linear systems. Systems Control Lett. 17 (1991), 9-14.
9. L. Fortuna, G. Nunnari and A. Gallo: Model Order Reduction Techniques with Applications in Electrical Engineering. Springer-Verlag, Berlin 1992.
10. K. Glover: All optimal Hankel-norm approximation of linear multivariable systems and their L∞-errors bounds. Internat. J. Control 39 (1984), 6, 1115-1193.
11. I. Gohberg, M. A. Kaashoek and L. Lerer: Minimality and realization of discrete time-varying systems. Oper. Theory: Adv. Appl. 56 (1992), 261-296.
12. O. M. Grasselli and S. Longhi: Disturbance localization by measurements feedback for linear periodic discrete-time systems. Automatica 24 (1988), 375-385.
13. O. M. Grasselli and S. Longhi: Zeros and poles of linear periodic discrete-time systems. Circuits Systems Signal Process. 7 (1988), 361-380.
14. O. M. Grasselli and S. Longhi: Robust tracking and regulation of linear periodic discrete-time systems. Internat. J. Control 54 (1991), 613-633.
15. O. M. Grasselli and S. Longhi: The geometric approach for linear periodic discrete-time systems. Linear Algebra Appl. 158 (1991), 27-60.
16. M. Gree and D. J. N. Limebeer: Linear Robust Control. Prentice Hall, Englewood Cliffs, N. J. 1995.
17. R. A. Mayer and C. S. Burrus: A unified analysis of multirate and periodically time-varying digital filters. Trans. Ccts Syst. CSA-22 (1975), 162-168.
18. B. C. Moore: Principal component analysis in linear systems: controllability, observability and modal reduction. Trans. Automat. Control AC-26 (1981), 17-32.
19. B. Park and E. I. Verriest: Canonical forms on discrete linear periodically time-varying systems and a control application. In: Proc. of the 28th IEEE Conference on Decision and Control, Tampa 1989, pp. 1220-1225.
20. L. Pernebo and L. M. Silverman: Model reduction via balanced state space representations. IEEE Trans. Automat. Control AC-27 (1982), 2, 382-387.
21. G. Salomon, K. Zhou and E. Wu: A new balanced realization and model reduction method for unstable systems. In: Proc. of 14th IFAC World Congress, Beijing 1999, vol. D, pp. 123-128.
22. S. Shokoohi, L. M. Silverman and P. Van Dooren: Linear time-variable systems: balancing and model reduction. Trans. Automat. Control AC-28 (1983), 8, 810-822.
23. S. Shokoohi, L. M. Silverman and P. Van Dooren: Linear time-variable systems: stability of reduced models. Automatica 20 (1984), 1, 59-67.
24. A. Varga: Periodic Lyapunov equations: some applications and new algorithms. Internat. J. Control 67 (1997), 69-87.
25. B. Xie, R. K. A. V. Aripirala and V. L. Syrmos: Model reduction of linear discrete-time periodic systems using Hankel-norm approximation. In: Proc. of IFAC 13th World Congress, San Francisco, 1996, pp. 245-250.