Passification of non-square linear systems and feedback Yakubovich-Kalman-Popov Lemma

European Journal of Control

Volumn 9, Issue 6, 2003, Pages 577-586

  Fradkov, Alexander ^a  

^a INSTITUTE OF PROBLEMS OF MECHANICAL ENGINEERING   (Russian Federation)

Author keywords

Linear systems; Passification; Passivity; Yakubovich Kalman Popov Lemma

Indexed keywords

DIFFERENTIAL EQUATIONS; FEEDBACK CONTROL;

PASSIFICATION; PASSIVITY; YAKUBOVICH-KALMAN-POPOV LEMMA;

LINEAR SYSTEMS;

EID: 33845403197     PISSN: 09473580     EISSN: None     Source Type: Journal    
DOI: 10.3166/ejc.9.577-586     Document Type: Article

References (41)

1. Abdallah C, Dorato P, Kami S. SPR design using feedback. In: Proceedings of the American Control Conference, Boston, MA. 1991, pp 1742-1743
2. Andrievsky BR, Churilov AN, Fradkov AL. Feedback Kalman-Yakubovich Lemma and its applications to adaptive control. In: Proceedings of the 35th IEEE Conference on Decision and Control, Kobe. December 1996, pp 4537-4542
3. Andrievsky BR, Fradkov AL, Kaufman H. Necessary and sufficient condition for almost strict positive realness and their application to direct implicit adaptive control. In: Proceedings of the American Control Conference, Baltimore. 1994, pp 1265-1266
4. Andrievsky BR, Stotsky AA, Fradkov AL. Velocity gradient algorithms in control and adaptation problems. A survey Autom Rem Control 1988; 49(12): 1533-1563
5. Bondarko VA, Fradkov AL. G-passification of infinite-dimensional linear systems. In: proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas. 2002, pp 3396-3401
6. Bondarko VA, Fradkov AL. Necessary and sufficient conditions for the passifiability of linear distributed systems. Autom Rem Control 2003; 64(4): 517-530
7. Byrnes CI, Isidori A, Willems JC. Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems. IEEE Trans Autom Control 1991; 36(11): 1228-1240
8. Fomin VN, Fradkov AL, Yakubovich VA. Adaptive control of dynamic objects. Nauka, Moscow, 1981 (in Russian)
9. Fradkov AL. Synthesis of an adaptive system for linear plant stabilization. Autom Rem Control 1974; 35(12): 1960-1966
10. Fradkov AL. Quadratic Lyapunov functions in the adaptive stabilization problem of a linear dynamic plant. Siberian Math J 1976; (2): 341-348
11. Fradkov AL. Adaptive control in complex systems. Nauka, Moscow, 1990 (in Russian)
12. Fradkov AL. Passification of nonsquare linear systems. In: Proceedings of the 5th European Control Conference, Porto. 2001, pp 3338-3343
13. Fradkov AL, Hill DJ. Exponential feedback passivity and stabilizability of nonlinear systems. Automatica 1998; 34(6): 697-703
14. Fradkov AL, Markov AYu. Adaptive synchronization of chaotic systems based on speed gradient method and passification. IEEE Trans Circ Syst 1997; 44(10): 905-912
15. Fradkov AL, Miroshnik IV, Nikiforov VO. Nonlinear and adaptive control of complex systems. Kluwer Academic Publishers, Dordrecht, 1999
16. Fradkov AL, Nijmeijer H, Markov AYu. Adaptive observer-based synchronization for communication. Int J Bifurcations Chaos 2000; 10(12): 2807-2814
17. Fradkov AL, Pogromsky AYu. Introduction to control of oscillations and chaos. World Scientific, Singapore, 1998
18. Gu G. Stabilizability conditions of multivariable uncertain systems via output feedback control. IEEE Trans Autom Control 1990; 35(8): 925-927
19. Hautus MLJ. Strong detectability and observers. Linear Algebra Appl. 1983; 50: 353-368
20. Hou M, Muller PC. Disturbance decoupled observer design: a unified viewpoint. IEEE Trans Autom Control 1994; 39(6): 1338-1341
21. Huang CH, Ioannou PI, Maroulas J, Safonov MG. Design of strictly positive real systems using constant output feedback. IEEE Trans Autom Control 1999; 44(3): 569-573
22. Ilchmann A. Non-identifier-based adaptive control of dynamic systems. Lecture Notes in Control and Information Science, Springer-Verlag, New York, 1993
23. Kaufman H, Bar-Kana I, Sobel K. Direct adaptive control algorithms. Springer, New York, 1994
24. Kokotović PV, Sussmann HJ. A positive real condition for global stabilization of nonlinear systems. Syst Contr Lett 1989; 13: 125-133
25. Lozano R, Brogliato B, Egeland O, Maschke B. Dissipative systems analysis and control. Springer-Verlag, London, 2000
26. Moreno J. Existence of unknown input observers and feedback passivity for linear systems. In: Proceedings of the 40th IEEE Conference on Decision and Control, Orlando. 2001, pp 3366-3371
27. Picci G, Pinzoni S. On feedback dissipative systems. J Math Syst. Contr 1992; 2(1): 1-30
28. Popov VM. On the problem in the theory of absolute stability of automatic control. Autom Rem Control 1964:25(9): 1129-1134
29. Saberi A, Kokotović PV, Sussmann HJ. Global stabilization of partially linear composite systems. SIAM J Contr Optimiz 1990; 28(6): 1491-1503
30. Saberi A, Sannuti P. Squaring down by static and dynamic compensators. IEEE Trans Autom Control 1988; 33(4): 358-365
31. Sepulchre R, Janković M, Kokotović PV. Constructive nonlinear control. Springer-Verlag, New York, 1996
32. Seron MM, Hill DJ, Fradkov AL. Adaptive passification of nonlinear systems. In: Proceedings of the 33rd Conference on Decision and Control, Lake Buena Vista. 1994, pp 190-195
33. Sobel K, Kaufman H, Mabius L. Implicit adaptive control for a class of MIMO systems. IEEE Trans Aerosp Electr Syst 1982; 18: 576-590
34. Steinberg A. A sufficient condition for output feedback stabilization on uncertain dynamical systems. IEEE Trans Autom Control 1988; 33(7): 676-677
35. Sun W, Khargonekar P, Shim D. Solution to the positive real control problem for linear time-invariant systems. IEEE Trans Autom Control 1994; 39(10): 2034-2046
36. Tsykunov AM. Adaptive control of systems with delay. Nauka, Moscow, 1984 (in Russian)
37. Weiss H, Wang Q, Speyer JL. System characterization of positive real conditions. IEEE Trans Autom Control 1994; 39(3): 540-544
38. Willems IC, Byrnes CI. Adaptive stabilization of multivariable linear system. In: Proceedings of the 23rd IEEE Conference on Decision and Control. 1984, pp 1574-1577
39. Yakubovich VA. The solution of certain matrix inequalities in automatic control theory. Soviet Math Dokl 1962; 3: 620-623
40. Yakubovich VA. Periodic and almost-periodic limit modes of controled systems with several, in general discontinuous, nonlinearities. Soviet Math Dokl 1966; 7(6): 1517-1521
41. Zeheb A. A sufficient condition for output feedback stabilization on uncertain systems. IEEE Trans Autom Control 1986; 31(11): 1055-1057