Nonlinear control design for linear differential inclusions via convex hull of quadratics

Automatica

Volumn 43, Issue 4, 2007, Pages 685-692

  Hu, Tingshu ^a  

^a University of Massachusetts   (United States)

Author keywords

Linear differential inclusion; Lyapunov functions; Nonlinear feedback; Robust performance; Robust stability

Indexed keywords

COMPUTATION THEORY; CONTROL THEORY; CONVERGENCE OF NUMERICAL METHODS; FEEDBACK CONTROL; LYAPUNOV METHODS; SYSTEM STABILITY;

BILINEAR MATRIX INEQUALITIES (BMI); LINEAR DIFFERENTIAL INCLUSION; LINEAR MATRIX INEQUALITY (LMI); NONLINEAR FEEDBACK; ROBUST PERFORMANCE;

NONLINEAR CONTROL SYSTEMS;

EID: 33847395722     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2006.10.015     Document Type: Article

References (20)

1. Blanchini F. Non-quadratic Lyapunov functions for robust control. Automatica 31 (1995) 451-461
2. Blanchini F., and Megretski A. Robust state feedback control of LTV systems: Nonlinear is better than linear. IEEE Transactions on Automatic Control 44 4 (1999) 802-807
3. Boyd, S., El Ghaoui, L., Feron, E., & Balakrishnan, V. (1994). Linear Matrix Inequalities in Systems and Control Theory. SIAM Studies in Applied Mathematics. Philadelphia: SIAM.
4. Chesi G., Garulli A., Tesi A., and Vicino A. Homogeneous Lyapunov functions for systems with structured uncertainties. Automatica 39 (2003) 1027-1035
5. Goebel, R., Hu, T., & Teel, A. R. (2005). Dual matrix inequalities in stability and performance analysis of linear differential/difference inclusions. In Current trends in nonlinear systems and control. Basel: Birkhauser.
6. Goebel R., Teel A.R., Hu T., and Lin Z. Conjugate convex Lyapunov functions for dual linear differential equations. IEEE Transactions on Automatic Control 51 4 (2006) 661-666
7. Hassibi, A., How, J., & Boyd, S. (1999). A path-following method for solving BMI problems in control. In Proceedings of American control conference (pp. 1385-1389).
8. Hu T., Goebel R., Teel A.R., and Lin Z. Conjugate Lyapunov functions for saturated linear systems. Automatica 41 11 (2005) 1949-1956
9. Hu T., and Lin Z. Composite quadratic Lyapunov functions for constrained control systems. IEEE Transactions on Automatic Control 48 (2003) 440-450
10. Hu T., and Lin Z. Properties of composite quadratic Lyapunov functions. IEEE Transactions on Automatic Control 49 (2004) 1162-1167
11. Hu T., and Lin Z. Absolute stability analysis of discrete-time systems with composite quadratic Lyapunov functions. IEEE Transactions on Automatic Control 50 (2005) 781-798
12. Hu T., Teel A.R., and Zaccarian L. Stability and performance for saturated systems via quadratic and non-quadratic Lyapunov functions. IEEE Transactions on Automatic Control 51 11 (2006) 1770-1786
13. Jarvis-Wloszek, Z., & Packard, A. K. (2002). An LMI method to demonstrate simultaneous stability using non-quadratic polynomial Lyapunov functions. In IEEE conference on decision and control, Las Vegas, NV (pp. 287-292).
14. ∞-optimal control with state-feedback. IEEE Transactions on Automatic Control 33 8 (1988) 786-788
15. Molchanov A.P. Criteria of asymptotic stability of differential and difference inclusions encountered in control theory. Systems and Control Letters 13 (1989) 59-64
16. Polanski A. Lyapunov function construction by linear programming. IEEE Transactions on Automatic Control 42 (1997) 1013-1016
17. Polanski A. On absolute stability analysis by polyhedral Lyapunov functions. Automatica 36 (2000) 573-578
18. Rockafellar R.T. Convex analysis (1970), Princeton University Press, Princeton, NJ
19. Xie L., Shishkin S., and Fu M. Piecewise Lyapunov functions for robust stability of linear time-varying systems. Systems and Control Letters 31 (1997) 165-171
20. Yfoulis C.A., and Shorten R. A numerical technique for the stability analysis of linear switched systems. International Journal of Control 77 (2004) 1019-1039