Stability analysis and control of a class of differential-algebraic nonlinear systems

International Journal of Robust and Nonlinear Control

Volumn 14, Issue 16, 2004, Pages 1301-1326

  Coutinho, D F ^a   Bazanella, A S ^b   Trofino, A ^c   Silva, A S E ^c  

^a PONTIFICAL CATHOLIC UNIVERSITY OF RIO GRANDE DO SUL   (Brazil)

^b FEDERAL UNIVERSITY OF RIO GRANDE DO SUL   (Brazil)

^c FEDERAL UNIVERSITY OF SANTA CATARINA   (Brazil)

Author keywords

Convex optimization; Differential algebraic systems; Domain of attraction; Nonlinear damping control

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; FREQUENCIES; SENSITIVITY ANALYSIS; SPECIFICATIONS; UNCERTAIN SYSTEMS; CONVEX OPTIMIZATION; DAMPING; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; NONLINEAR SYSTEMS;

PID CONTROL; POLYTOPIC DESIGNS; REDUCED-ORDER CONTROLLERS; UNSTRUCTURED UNCERTAINTY; ANALYSIS AND CONTROLS; CONTROL DESIGN; DIFFERENTIAL ALGEBRAIC; DIFFERENTIAL ALGEBRAIC SYSTEMS; DOMAIN OF ATTRACTION; NONLINEAR DAMPING; POLYNOMIAL LYAPUNOV FUNCTION; STABILITY ANALYSIS;

CONTROL EQUIPMENT; ALGEBRA;

EID: 84960927512     PISSN: 10498923     EISSN: None     Source Type: Journal    
DOI: 10.1002/rnc.950     Document Type: Article

References (27)

1. Chiang H-D, Thorp JS. Stability regions of nonlinear dynamical systems: a constructive methodology. IEEE Transactions on Automatic Control 1989; 34(12):1229-1241.
2. Brockett RW. Asymptotic stability and feedback stabilization. In Differential Geometric Control Theory (Progress in Mathematics), Brockett RW, Millmann RS, Sussmann HJ, (eds). Birkhauser: Basel, 1983.
3. Bazanella A, Kokotovic P, e Silva A. Lyapunov design of excitation control for synchronous machines. In Proceedings of the 36th IEEE Conference on Decision and Control, San Diego, 1997.
4. Zaborsky J, Huang G, Zheng B, Leung T-C. On the phase portrait of a class of large nonlinear dynamic systems such as the power system. IEEE Transactions on Automatic Control 1988; 33(1):4-15.
5. Bernstein DS, Michel AN. A chronological bibliography on saturating actuators. International Journal of Robust and Nonlinear Control 1995; 5:375-380.
6. Jirstrand M. Invariant sets for a class of hybrid systems. Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, 1998.
7. Fischman A, Bazanella A, Silva AS, Dion JM, Dugart L. Guaranteed cost control with application to power systems. Proceedings of the 2nd IFAC Symposium on Robust Control Design, Bucarest, 1998.
8. Bazanella A, Paim CC, Robust design of power systems damping controllers. Proceedings of the IEEE Power Tech'99 Conference, Budapest, 1999.
9. Trofino A. Robust stability and domain of attraction of uncertain nonlinear systems. Proceedings of the American Control Conference, Chicago, 2000.
10. Coutinho DF, Trofino A, Fu M. Guaranteed cost control of uncertain nonlinear systems via polynomial Lyapunov functions. Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, 2001.
11. Chiang H-S, Chu C-C, Cauley G. Direct stability analysis of electric power systems using energy functions: theory, applications, and perspective. In Proceedings of the IEEE: Special Issue on Nonlinear Phenomena in Power Systems, Hill DJ (ed.). IEEE Inc.: New York, 1995.
12. Boyd S, El Ghaoui L, Feron E, Balakrishnan V. Linear Matrix Inequalities in Systems and Control Theory. SIAM books: Philadelphia, 1994.
13. Khalil HK. Nonlinear Systems. Prentice-Hall: Eaglewood Clifis, NJ, 1996.
14. Chang TN, Davison EJ. Decentralized control of descriptor systems. IEEE Transactions on Automatic Control 2001; 46(10):1589-1595.
15. Bender DJ, Laub AJ. The linear quadratic optimal regulator for descriptor systems. IEEE Transactions on Automatic Control 1997; 32(8):672-688.
16. Arrilaga J, Arnold CP, Harker BJ. Computer Modeling of Electrical Power Systems. Wiley: New York, 1983.
17. Pai MA. Power System Stability. North-Holland Publishing Company: Amsterdam, 1981.
18. Trofino A. Local, regional and global stability: an LMI approach for uncertain nonlinear systems. Technical Report (submitted to Automatica), Department of Automation and Systems, UFSC, Florianópolis-SC, Brazil, November 2001.
19. Huang Y, Jadbabaie A. Nonlinear H∞ control: an enhanced quasi-LPV approach. Proceedings of the 14th IFAC World Congress, Beijing, 1999; 85-90.
20. Trofino A. Bi-quadratic stability for nonlinear systems. Proceedings of the 3rd IFAC Symposium on Robust Control Design, Prague, 2000.
21. Finsler P. Über das Vorkmmen Definiter and Semi-definiter Formen in Scharen Quadratischer Formen. Comentartii Mathematici Helvetici 1937; 9:188-192.
22. Pare TE, Hindi H, How JP, Boyd SP. Synthesizing stability regions for systems with saturating actuators. Proceedings of the 37th IEEE Conference on Decision and Control, vol. 2, Tampa, 1998; 1981-1982.
23. Davison EJ, Kurak EM. A computational method for determining quadratic Lyapunov functions for non-linear systems. Automatica 1971; 7:627-636.
24. Sepulchre R, Jankovic M, Kokotovic PV. Constructive Nonlinear Control. Springer Berlin, 1996.
25. Bazanella A, Kokotovic P, e Silva A. A dynamic extension for LgV controllers. IEEE Transactions on Automatic Control 1999; 44:588-592.
26. Fan MKH, Tits AL, Doyle JC. Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics. IEEE Transactions on Automatic Control 1991; 36(1):25-38.
27. Feron E, Apkarian P, Gahinet P. Analysis and synthesis of robust control systems via parameter-dependent Lyapunov functions. IEEE Transactions on Automatic Control 1996; 41(7):1041-1046.