Output dead beat control for a class of planar polynomial systems

SIAM Journal on Control and Optimization

Volumn 36, Issue 1, 1998, Pages 253-272

  Nesic D ^a   Mareels, I M Y ^a   Bastin, G ^b   Mahony, R ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b Batiment Euler   (Belgium)

Author keywords

Controllability; Dead beat; Polynomial systems

Indexed keywords

ALGORITHMS; CONTROL SYSTEM ANALYSIS; CONTROLLABILITY; DIFFERENCE EQUATIONS; FEEDBACK CONTROL; NONLINEAR CONTROL SYSTEMS; POLYNOMIALS; STATE SPACE METHODS;

OUTPUT DEAD BEAT CONTROL; PLANAR POLYNOMIAL SYSTEMS;

DISCRETE TIME CONTROL SYSTEMS;

EID: 0031676699     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012995286381     Document Type: Article

References (24)

1. G. BASTIN, F. JARACHI, AND I.M.Y. MAREELS, Dead beat control of recursive nonlinear systems, in Proc. 32nd IEEE Conference on Decision and Control, San Antonio, TX, 1993, pp. 2965-2971.
2. F. JARACHI, G. BASTIN, AND I.M.Y. MAREELS, One-step ahead control of nonlinear discrete time systems with one dimensional zero dynamics: Global stability conditions, in Proc. NOLCOS-III, Tahoe City, CA, June 26-28, 1995, pp. 848-852.
3. G. BASTIN, F. JARACHI, AND I.M.Y. MAREELS, Output deadbeat control of nonlinear discrete time systems with one dimensional zero dynamics: Global stability conditions, submitted to IEEE Trans. Automat. Control, 1997.
4. R. BENEDETTI AND J.J. RISLER, Real Algebraic and Semi-Algebraic Sets, Hermann, Paris, 1990.
5. S.A. BILLINGS AND W.S.F. VOON, A prediction-error and stepwise-regression estimation algorithm for non-linear systems, Internat. J. Control, 44 (1986), pp. 803-822.
6. D. COX, J. LITTLE, AND D. O'SHEA, Ideals, Varieties and Algorithms, Springer-Verlag, New York, Berlin, 1992.
7. M.E. EVANS AND D.N.P. MURTHY, Controllability of a class of discrete time bilinear systems, IEEE Trans. Automat. Control, 22 (1977), pp. 78-83.
8. M.E. EVANS AND D.N.P. MURTHY, Controllability of discrete time inhomogeneous bilinear systems, Automatica J. IFAC, 14 (1978), pp. 147-151.
9. S.T. GLAD, Output dead-beat control for nonlinear systems with one zero at infinity, Systems Control Lett., 9 (1987), pp. 249-255.
10. S.T. GLAD, Dead beat control for nonlinear systems, in Analysis and Control of Nonlinear Systems, C.I. Byrnes, C.F. Martin, and R.E. Saeks, eds., North-Holland, Amsterdam, 1988, pp. 437-442.
11. T. GOKA, T.J. TARN, AND J. ZABORSZKY, On the controllability of a class of discrete bilinear systems, Automatica J. IFAC, 9 (1973), pp. 615-622.
12. O.M. GRASSELLI, A. ISIDORI, AND F. NICOLO, Dead-beat control of discrete-time bilinear systems, Internat. J. Control, 32 (1980), pp. 31-39.
13. R. HABER AND H. UNBEHAUEN, Structure identification of nonlinear dynamic systems - A survey of input/output approaches, Automatica, 26 (1990), pp. 651-677.
14. R. HABER AND L. KEVICZKY, Identification of nonlinear dynamic systems, in Proc. 4th IFAC Symp. on Identification and System Parameter Estimation, Tbilisi, USSR, 1978, pp. 79-126.
15. V.L. KOCIC AND G. LADAS, Global Behaviour of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic Publishers, Dordrecht, 1993.
16. J. O'REILLY, The discrete linear time invariant time-optimal control problem - An overview, Automatica J. IFAC, 17 (1981), pp. 363-370.
17. S. MONACO AND D. NORMAND-CYROT, Minimum-phase nonlinear discrete-time systems, in Proc. 28th Conference on Decision and Control, Los Angeles, CA, 1987, pp. 979-986.
18. S. MONACO AND D. NORMAND-CYROT, Zero dynamics of sampled nonlinear systems, Systems Control Lett., 11 (1988), pp. 229-234.
19. N. ROUCHE, P. HABETS, AND M. LALOY, Stability Theory by Liapunov's Direct Method, Springer-Verlag, Berlin, 1977.
20. D. NEŠIĆ, I.M.Y. MAREELS, R. MAHONY, AND G. BASTIN, v-step controllability of polynomial scalar systems, in Proc. 3rd ECCC, Rome, Italy, 1994, pp. 277-282.
21. D. NEŠIĆ AND I.M.Y. MAREELS, Dead beat control of polynomial scalar systems, submitted to Automatica J. IFAC, 1996.
22. D. NEŠIĆ, I.M.Y. MAREELS, G. BASTIN, AND R. MAHONY, Necessary and sufficient conditions for output dead beat controllability for a class of polynomial systems, in Proc. 34th CDC, New Orleans, LA, 1995, pp. 7-12.
23. E.D. SONTAG, Polynomial Response Maps, Springer-Verlag, Berlin, New York, 1979.
24. E.D. SONTAG AND Y. ROUCHALEAU, On discrete-time polynomial systems, Nonlinear Anal., 1 (1976), pp. 55-64.