Globally stabilizing feedback control of process systems in generalized Lotka-Volterra form

Journal of Process Control

Volumn 18, Issue 1, 2008, Pages 80-91

  Magyar, A ^a   Szederkenyi G ^a   Hangos, K M ^a  

^a INSTITUTE FOR COMPUTER SCIENCE AND CONTROL   (Hungary)

Author keywords

Bilinear matrix inequalities; Nonlinear process systems; Quasi polynomial systems

Indexed keywords

ALGORITHMS; CONTROL EQUIPMENT; LINEAR MATRIX INEQUALITIES; PROBLEM SOLVING; PROCESS ENGINEERING;

BILINEAR MATRIX INEQUALITIES; ITERATIVE LINEAR MATRIX INEQUALITY (ILMI) ALGORITHM; QUASI-POLYNOMIAL SYSTEMS;

FEEDBACK CONTROL;

EID: 36749034941     PISSN: 09591524     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jprocont.2007.05.003     Document Type: Article

References (26)

1. Cao Y.-Y., Lam J., and Sun Y.-X. Static output feedback stabilization: an ILMI approach. Automatica 12 (1998) 1641-1645
2. Christofides P.D., and El-Farra N. Control of Nonlinear and Hybrid Process Systems: Designs for Uncertainty, Constraints and Time-Delays (2005), Springer-Verlag
3. Henson M., and Seborg D. Nonlinear Process Control (1997), Prentice-Hall, NJ
4. Findeisen R., Imsland L., Allgöwer F., and Foss B. State and output feedback nonlinear model predictive control: an overview. European Journal of Control 9 (2003) 2-3
5. Kravaris C., and Kantor J. Geometric methods for nonlinear process control: 2. Controller synthesis. Industrial and Engineering Chemistry Research 29 (1990) 2310-2323
6. Chen Y., Manousiouthakis V., and Edgar T. Globally optimal nonlinear feedback: application to nonisothermal CSTR control. Chemical Engineering Communications 193 (2006) 233-245
7. Hernández-Bermejo B., Fairén V., and Brenig L. Algebraic recasting of nonlinear ODEs into universal formats. Journal of Physics A - Mathematical and General 31 (1998) 2415-2430
8. Figueiredo A., Gleria I.M., and Rocha T.M. Boundedness of solutions and Lyapunov functions in quasi-polynomial systems. Physics Letters A 268 (2000) 335-341
9. Hernández-Bermejo B. Stability conditions and Lyapunov functions for quasi-polynomial systems. Applied Mathematics Letters 15 (2002) 25-28
10. Szederkényi G., and Hangos K. Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems. Physics Letters A 324 (2004) 437-445
11. Szederkényi G., Hangos K., and Magyar A. On the time-reparametrization of quasi-polynomial systems. Physics Letters A 334 (2005) 288-294
12. J. Gouzé, Global stabilization of n-dimensional population models by a positive control, in: Proceedings of the 33rd IEEE Conference on Decision and Control, Orlando, USA, 1994, pp. 1335-1336.
13. F. Grognard, J. Gouzé, Positive control of Lotka-Volterra systems, in: Proceedings of 16th IFAC World Congress, Prague, Czech Republic, 2005, on CD.
14. A. Magyar, G. Szederkényi, K.M. Hangos, Quasi-polynomial system representation for the analysis and control of nonlinear systems, in: Proceedings of 16th IFAC World Congress, 2005, on CD.
15. Figueiredo A., Gleria I.M., and Filho T.M.R. A numerical method for the stability analysis of quasi-polynomial vector fields. Nonlinear Analysis 52 (2003) 329-342
16. Van Antwerp J., and Braatz R. A tutorial on linear and bilinear matrix inequalities. Journal of Process Control 10 (2000) 363-385
17. Hernández-Bermejo B., and Fairén V. Lotka-Volterra representation of general nonlinear systems. Mathematical Biosciences 140 (1997) 1-32
18. Hernández-Bermejo B., and Fairén V. Nonpolynomial vector fields under the Lotka-Volterra normal form. Physics Letters A 206 (1995) 31-37
19. Hangos K.M., Bokor J., and Szederkényi G. Analysis and Control of Nonlinear Process Systems (2004), Springer-Verlag
20. Boyd S., Ghaoui L.E., Feron E., and Balakrishnan V. Linear Matrix Inequalities in System and Control Theory (1994), SIAM, Philadelphia
21. C. Scherer, S. Weiland, Linear Matrix Inequalities in Control, DISC, http://w3.ele.tue.nl/nl/mbs/cs/education/courses/DISClmi/, 2006.
22. Kocvara M., and Stingl M. A code for convex nonlinear and semidefinite programming. Optimization Methods and Software 8 (2003) 317-333
23. Tuan H., Apkarian P., and Nakashima Y. A new Lagrangian dual global optimization algorithm for solving bilinear matrix inequalities. International Journal of Robust and Nonlinear Control 10 (2000) 561-578
24. M. Kocvara, M. Stingl, TOMLAB/PENBMI solver (Matlab Toolbox), PENOPT Gbr., 2005.
25. Kaszkurewicz X., and Bhaya Y. Matrix Diagonal Stability in Systems and Computation (2000), Birkhäuser
26. Coutinho M.F.D., and Trofino A. Guaranteed cost control of uncertain nonlinear systems via polynomial Lyapunov functions. IEEE Transactions on Automatic Control 47 (2002) 1575-1580