Improved state feedback controller synthesis for piecewise-linear systems

International Journal of Innovative Computing, Information and Control

Volumn 8, Issue 10 A, 2012, Pages 6945-6957

  Liu, Kai ^a,b   Yao, Yu ^a   Sun, Dengfeng ^b   Balakrishnan, Venkataramanan ^b  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b PURDUE UNIVERSITY   (United States)

Author keywords

Continuous controller; Linear matrix inequalities; Piecewise quadratic Lyapunov function; Piecewise linear systems; Sliding motion

Indexed keywords

ASYMPTOTICAL STABILITY; ASYMPTOTICALLY STABLE; CONTINUOUS CONTROLLER; CONTROL DESIGN; INVERTED PENDULUM; LINEAR MATRIX; NUMERICAL OPTIMIZATIONS; PIECE-WISE LINEAR SYSTEMS; PIECE-WISE QUADRATIC LYAPUNOV FUNCTION; PIECEWISE AFFINE CONTROLLERS; SLIDING MOTIONS; STATE FEEDBACK CONTROLLER;

CLOSED LOOP SYSTEMS; FEEDBACK CONTROL; LINEAR MATRIX INEQUALITIES; LINEAR SYSTEMS; LYAPUNOV FUNCTIONS; NONLINEAR CONTROL SYSTEMS; STATE FEEDBACK;

PIECEWISE LINEAR TECHNIQUES;

EID: 84866040689     PISSN: 13494198     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (23)

1. R. Wang and J. Zhao, Exponential stability analysis for discrete-time switched linear systems with time-delay, International Journal of Innovative Computing, Information and Control, vol.3, no.6(B), pp.1557-1564, 2007.
2. E. Sontag, Nonlinear regulation: The piecewise linear approach, IEEE Trans. Automatic Control, vol.26, no.2, pp.346-358, 1981.
3. K. Liu, D. F. Sun, Y. Yao and V. Balakrishnan, Controller synthesis for a class of uncertain nonlinear systems: A piecewise linear differential inclusion approach, Proc. of IEEE Multi-Conference on Systems and Control, Denver, USA, 2011.
4. M. Johansson and A. Ranter, Computation of piecewise quadratic lyapunov functions for hybrid systems, IEEE Trans. Automatic Control, vol.43, no.4, pp.555-559, 1998.
5. A. Hassibi and S. Boyd, Quadratic stabilization and control of piecewise-linear systems, Proc. of American Control Conf., Philadelphia, USA, pp.3659-3664, 1998.
6. S. Boyd, L. E. Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, SIAM, 1994.
7. D. Ding and G. Yang, State-feedback control design for continuous-time piecewise-linear systems: An LMI approach, Proc. of American Control Conf., Seattle, Washington, USA, pp.1104-1108, 2008.
8. G. Feng, Controller design and analysis of uncertain piecewise linear systems, IEEE Trans. Circuits System, vol.49, pp.224-232, 2002.
9. ∞ controller synthesis of uncertain piecewise linear system, IET Control Theory and Applications, vol.151, pp.295-301, 2004.
10. Y. Zhu, D. Li and G. Feng, H-infinity controller synthesis of uncertain piecewise continuous-time linear systems, IET, Control Theory and Applications, vol.152, pp.513-519, 2005.
11. ∞ controller design for continuous-time piecewise linear systems with linear fractional uncertainties, Nonlinear Analysis: Hybrid Systems, vol.2, pp.1264-1274, 2008.
12. A. BenAbdallah, M. A. Hammami and J. Kallel, Robust stability of uncertain piecewise-linear systems: LMI approach, Nonlinear Analysis: Hybrid Systems, vol.63, pp.183-192, 2010.
13. ∞ control for uncertain piecewise linear systems, Journal of Dynamical and Control Systems, vol.14, no.1, pp.121-144, 2008.
14. J. X. Zhang and W. S. Tang, Output feedback optimal guaranteed cost control of uncertain piecewise linear systems, International Journal of Robust and Nonlinear Control, vol.19, pp.569-590, 2009.
15. Q. Sang and G. Tao, State-feedback control design for continuous-time piecewise-linear systems: An LMI approach, Proc. of American Control Conf., Baltimore, MD, USA, pp.4040-4045, 2010.
16. K. Liu, D. F. Sun, Y. Yao and V. Balakrishnan, Adaptive control design for piecewise-linear systems with parameter uncertainties, Proc. IEEE Conf. on Decision and Control, Orlando, FL, USA, 2011.
17. L. Rodrigues, Dynamic Output Feedback Controller Synthesis for Piecewise-Affine Systems, Ph.D. Thesis, Stanford, 2002.
18. J. Imura and A. V. D. Schaft, Characterization of well-posedness of piecewise-linear systems, IEEE Trans. Automatic Control, vol.45, no.9, pp.1600-1619, 2000.
19. X. Xia, Well-posedness of piecewise-linear systems with multiple modes and multiple criteria, IEEE Trans. Automatic Control, vol.47, no.10, pp.1716-1720, 2002.
20. J. Imura, Well-posedness analysis of switch-driven hybrid systems, IEEE Trans. Automatic Control, vol.48, no.11, pp.1926-1935, 2003.
21. Y. Yao, K. Zheng, K. M. Ma and T. L. Shen, Sliding mode control design based on new approaching criteria for linear lipschitz switching surface, International Journal of Modeling, Identification and Control, vol.7, no.3, pp.294-304, 2009.
22. W. Yue, Odeling and Piecewise-Ane Control of an Aerobatic Helicopter, Concordia University, 2005.
23. J. P. Hespanha, Linear System Theory, Princeton University Press, 2009.