Piecewise-affine Lyapunov functions for discrete-time linear systems with saturating controls

Automatica

Volumn 38, Issue 12, 2002, Pages 2177-2184

  Milani, Basílio E A ^a  

^a UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

Actuator saturation; Discrete time systems; Linear programming; Lyapunov functions; Stability regions

Indexed keywords

ACTUATORS; ALGORITHMS; CLOSED LOOP CONTROL SYSTEMS; LINEAR PROGRAMMING; LYAPUNOV METHODS; PIECEWISE LINEAR TECHNIQUES; POLYNOMIALS; SYSTEM STABILITY;

STABILITY REGIONS;

DISCRETE TIME CONTROL SYSTEMS;

EID: 0036888262     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0005-1098(02)00193-0     Document Type: Article

References (17)

1. Bitsoris G., Gravalou E. Comparison principle, positive invariance and constrained regulation of nonlinear systems. Automatica. 31(2):1995;217-222.
2. Blanchini F. Ultimate boundedness control for uncertain discrete-time systems via set-induced Lyapunov functions. IEEE Transactions on Automatic Control. 39(2):1994;428-433.
3. Chiang H., Thorp J.S. Stability regions of nonlinear dynamical systems. A constructive methodology IEEE Transactions on Automatic Control. 34(12):1989;1229-1241.
4. Dorea C.E.T., Hennet J.C. (A,B) -invariant polyhedral sets of linear discrete-time systems Journal of Optimization Theory and Applications. 103(3):1999;521-542.
5. Genesio R., Tartaglia M., Vicino A. On the estimation of asymptotic stability regions. State of the art and new proposals IEEE Transactions on Automatic Control. 30(8):1985;747-755.
6. Gomes da Silva J.M. Jr., Tarbouriech S. Polyhedral regions of local asymptotic stability for discrete-time linear systems with saturating controls. IEEE Transactions on Automatic Control. 44(11):1999;2081-2085.
7. Hennet J.C. Une extension du lemme de Farkas et son application au problème de regulation linéaire sous contraintes. Comptes Rendus de l'Academie des Sciences Paris. 308(I):1989;415-419.
8. Johansson M., Rantzer A. Computation of piecewise quadratic Lyapunov functions for hybrid systems. IEEE Transactions on Automatic Control. 43(4):1998;555-559.
9. Kiendl H., Adamy J., Stelzner P. Vector norms as Lyapunov functions for linear systems. IEEE Transactions on Automatic Control. 37(6):1992;839-842.
10. Milani, B.E.A. (1999). Contractive polyhedra for discrete-time linear systems with saturating controls. In Proceedings of 38th CDC, Phoenix, AZ (pp. 2039-2044).
11. Milham C.B. Fast feasibility methods for linear programming. OPSEARCH. 13(3-4):1976;198-204.
12. Romanchuck B.G. Computing regions of attractions with polytopes. Planar case Automatica. 32(12):1996;1727-1732.
13. Slotine J.E., Li W. Applied nonlinear control. 1981;Prentice-Hall, Englewood Cliffs, NJ.
14. Sussmann H., Sontag E.D., Yang Y. A general result on the stabilization of linear systems using bounded controls. IEEE Transactions on Automatic Control. 39(12):1994;2411-2424.
15. Tarbouriech, S., & Gomes da Silva Jr., J.M. (1997). Admissible polyhedra for discrete-time linear systems with saturating controls. In Proceedings of ACC, Albuquerque, NM (pp. 3915-3919).
16. Vassilaki M., Hennet J.C., Bitsoris G. Feedback control of linear discrete-time systems under state and control constraints. International Journal of Control. 47(6):1988;1727-1735.
17. Wright J.S. Primal-dual interior-point methods. 1997;SIAM, Philadelphia, PA.