Robust stability of uncertain piecewise-linear systems: LMI approach

Nonlinear Dynamics

Volumn 63, Issue 1-2, 2011, Pages 183-192

  Benabdallah, Abdallah ^a   Hammami, Mohamed Ali ^c   Kallel, Jalel ^b  

^a University of Sfax   (Tunisia)

^b University of Sfax   (Tunisia)

^c NONE

Author keywords

Linear matrix inequalities; Lyapunov function; Piecewise uncertain linear systems; Robust stability

Indexed keywords

HOMOGENEOUS POLYNOMIALS; ILLUSTRATIVE EXAMPLES; LMI APPROACH; LYAPUNOV; PIECE-WISE; PIECE-WISE LINEAR SYSTEMS; PIECEWISE UNCERTAIN LINEAR SYSTEMS; PIECEWISE-LINEAR; ROBUST STABILITY; SUFFICIENT CONDITIONS; TIME INVARIANTS;

DIFFERENTIAL EQUATIONS; FEEDBACK; LINEAR CONTROL SYSTEMS; LYAPUNOV FUNCTIONS; PIECEWISE LINEAR TECHNIQUES; POLYNOMIALS; STATE FEEDBACK; SYSTEM STABILITY;

LINEAR MATRIX INEQUALITIES;

EID: 78650775007     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-010-9795-2     Document Type: Article

References (17)

1. A. BenAbdallah M. Dlala M.A. Hammami 2007 A new Lyapunov function for stability of time-varying nonlinear perturbed systems Syst. Control Lett. 56 179 187 1114.93083 10.1016/j.sysconle.2006.08.009 2296644 (Pubitemid 46123622)
2. Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in Systems and Control Theory. SIAM Studies in Appl. Mathematics, SIAM, Philadelphia (1994)
3. P.A. Bliman 2004 An existence result for polynomial solutions of parameter-dependent LMIs Syst. Control Lett. 51 165 169 1157.93360 10.1016/j.sysconle.2003.08.001 2037250
4. Bliman, P.A., Oliveira, R.C.L.F., Montagner, V.F., Peres, P.L.D.: Existence of homogeneous polynomial solutions for parameter-dependent linear matrix inequalities with parameters in the simplex. In: Proceedings of the 45th IEEE Conference on Decision and Control, San Diego, CA, December, pp. 1486-1491 (2006)
5. Chesi, G., Garulli, A., Tesi, A., Vicino, A.: Robust stability of polytopic systems via polynomially parameter-dependent Lyapunov functions. In: Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, HI, pp. 4670-4675 (2003)
6. G. Chesi A. Garulli A. Tesi A. Vicino 2007 Homogeneous Lyapunov functions for systems with structured uncertainties Automatica 43 309 316 1111.93064 10.1016/j.automatica.2006.08.024 2281835 (Pubitemid 46037598)
7. Ding, D.-W., Yang, G.-H.: State-feedback control design for continuous-time piecewise linear systems: an LMI approach. In: Proceedings of the American Control Conference (2008)
8. P. Gahinet P. Apkarian M. Chilali 1996 Affine parameter dependent Lyapunov functions and real parametric uncertainty IEEE Trans. Autom. Control 41 3 436 442 0854.93113 10.1109/9.486646 1382994
9. G. Feng 2002 Controller design and analysis of uncertain piecewise-linear systems IEEE Trans. Circuits Systems I, Fundam. Theory Appl. 49 2 224 232 10.1109/81.983869 (Pubitemid 34291473)
10. Hassibi, A., Boyd, S.: Quadratic stabilization and control of piecewise-linear systems. In: American Control Conference, pp. 3659-3664 (1998)
11. M. Johansson A. Rantzer 1998 Computation of piecewise quadratic Lyapunov functions for hybrid systems IEEE Trans. Autom. Control 43 4 555 559 0905.93039 10.1109/9.664157 1617547
12. Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice-Hall, Englewood Cliffs (2002)
13. Montagner, V.F., Oliveira, R.C.L.F., Calliero, T.R., Borges, R.A., Peres, P.L.D., Prieur, C.: Robust absolute stability and stabilization based on homogeneous polynomially parameter-dependent Lur'e functions. In: ACC 2007. New York, NY (2007)
14. V.F. Montagner R.C.L.F. Oliveira T.R. Calliero R.A. Borgesb P.L.D. Peres C. Prieur 2009 Robust absolute stability and nonlinear state feedback stabilization based on polynomial Lur'e functions Nonlinear Anal. 70 5 1803 1812 1155.93408 10.1016/j.na.2008.02.081 2492119
15. R.C.L.F. Oliveira P.L.D. Peres 2006 LMI conditions for robust stability analysis based on polynomially parameter-dependent Lyapunov functions Syst. Control Lett. 55 52 61 1129.93485 10.1016/j.sysconle.2005.05.003 2185593 (Pubitemid 41737282)
16. Xu, J., Xie, L.: Homogeneous polynomial Lyapunov functions for piecewise affine systems. In: American Control Conference, June 8-10 (2005)
17. Yakubovich, V.A., Leonov, G.A., Gelig, A.Kh.: Stability of Stationary Sets in Control Systems with Discontinuous Nonlinearities. World Scientific, Singapore (2010)