Generation of stable limit cycles in controllable linear systems

Systems and Control Letters

Volumn 28, Issue 1, 1996, Pages 43-48

  Bacciotti, A ^a   Mazzi, L ^a   Sabatini, M ^b  

^a POLITECNICO DI TORINO   (Italy)

^b UNIVERSITY OF TRENTO   (Italy)

Author keywords

Li nard equation; Limit cycles; Linear control systems; Nonlinear feedback stabilization; Orbital Stability

Indexed keywords

EID: 0345880007     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-6911(96)00005-9     Document Type: Article

References (13)

1. D.K. Arrowsmith and C.M. Place, Ordinary Differential Equations (Chapman & Hall, London, 1982).
2. A. Bacciotti, Local Stabilizability of Nonlinear Control Systems (World Scientific, Singapore, 1992).
3. A. Bacciotti and L. Mazzi, Floquet theory and stabilization of periodic solutions, Rev. Roum. Math. Pures Appl. 39 (1994) 285-293.
4. A. Bacciotti and L. Mazzi, Stabilizability of closed orbits, Systems Control Lett. 24 (1994) 97-101.
5. T.R. Blows and N.G. Lloyd, The number of limit cycles of certain polynomial differential equations, Proc. Roy. Soc. Edinburgh 98 (1984) 215-239.
6. J.R. Graef, On the generalized Liénard equation with negative damping, J. Diff. Eq. 12 (1972) 34-62.
7. W. Hahn, Stability of Motion (Springer, Berlin, 1967).
8. S. Lefschetz, Differential Equations: Geometric Theory (Wiley, New York, 1962).
9. Y. Lin, E.D. Sontag and Y. Wang, Recent results on Lyapunov-theoretic techniques for nonlinear stability, Report Sycon-93-09, 1993.
10. L. Mazzi and V. Tabasso, On stabilization of time-dependent affine control systems, Rend. Sem. Mat. Univ. Polit. Torino, to appear.
11. T. Nadzieja, Construction of a smooth Lyapunov function for an asymptotically stable set, Czech. Math. J. 40 (1990) 115, 195-199.
12. E.D. Sontag, Mathematical Control Theory (Springer, Berlin, 1990).
13. F.W. Wilson, Smoothing derivatives of functions and applications, Trans. Am. Math. Soc. 139 (1969) 413-428.