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Switching LPV control designs using multiple parameter-dependent Lyapunov functions. (English) Zbl 1133.93370
Summary: We study the switching control of linear parameter-varying (LPV) systems using multiple parameter-dependent Lyapunov functions to improve performance and enhance control design flexibility. A family of LPV controllers is designed, each suitable for a specific parameter subregion. They are switched so that the closed-loop system remains stable and its performance is optimized. Two switching logics, hysteresis switching and switching with average dwell time, are examined. The control synthesis conditions for both switching logics are formulated as matrix optimization problems, which are generally non-convex but can be convexified under some simplifying assumptions. The hysteresis switching LPV control scheme is then applied to an active magnetic bearing problem.

93D30Scalar and vector Lyapunov functions
15A39Linear inequalities of matrices
LMI toolbox
Full Text: DOI
[1] Apkarian, P.; Gahinet, P.: A convex characterization of gain-scheduled H$\infty $controllers. IEEE transactions on automatic control 40, 853-864 (1995) · Zbl 0826.93028
[2] Becker, G. (1996). Additional results on parameter-dependent controllers for LPV systems. Proceedings of the 13th IFAC world congress (pp. 351-356).
[3] Becker, G.; Packard, A.: Robust performance of linear parametrically varying systems using parametrically-dependent linear feedback. Systems and control letters 23, 205-215 (1994) · Zbl 0815.93034
[4] Boyd, S. P.; Yang, Q.: Structured and simultaneous Lyapunov functions for system stability problems. International journal of control 50, 2215-2240 (1989) · Zbl 0683.93057
[5] Branicky, M.: Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE transactions on automatic control 43, No. 4, 475-482 (1998) · Zbl 0904.93036
[6] Decarlo, R. A.; Branicky, M. S.; Pettersson, S.; Lennartson, B.: Perspectives and results on the stability and stabilizability of hybrid systems. Proceedings of IEE 88, No. 7, 1069-1082 (2000)
[7] Gahinet, P.; Nemirovskii, A.; Laub, A. J.; Chilali, M.: LMI control toolbox. (1995)
[8] Hespanha, J. P.; Liberzon, D.; Morse, A. S.: Hysteresis-based switching algorithm for supervisory control of uncertain systems. Automatica 39, 263-272 (2003) · Zbl 1011.93500
[9] Hespanha, J. P., & Morse, A. S. (1999). Stability of switched systems with average dwell-time. Proceedings of the 38th IEEE conference on decision control (pp. 2655-2660).
[10] Johansson, M.; Ranzer, A.: Computation of piecewise quadratic Lyapunov functions for hybrid systems. IEEE transactions on automatic control 43, No. 4, 555-559 (1998) · Zbl 0905.93039
[11] Liberzon, D.: Switching in systems and control. (2003) · Zbl 1036.93001
[12] Lim, S. (1999). Analysis and control of linear parameter-varying systems. Ph.D. dissertation, Stanford University.
[13] Lim, S., & Chan, K. (2003). Stability analysis of hybrid linear parameter-varying systems. Proceedings of the 2003 American control conference (pp. 4822-4827).
[14] Malmborg, J., Bernhardsson, B., & Astrom, K. J. (1996). A stabilizing switching scheme for multi-controller systems. Proceedings of the IFAC world congress.
[15] Mohamed, A. M.; Busch-Vishmiac, I.: Imbalance compensation and automation balancing in magnetic bearing systems using the Q-parameterization theory. IEEE transactions on control system technology 3, No. 2, 202-211 (1995)
[16] Packard, A. K.: Gain scheduling via linear fractional transformations. Systems and control letters 22, No. 2, 79-92 (1994) · Zbl 0792.93043
[17] Peleties, P., & Decarlo, R. (1991). Asymptotic stability of m-switched systems using Lyapunov-like functions. Proceedings of the American control conference (pp. 1679-1684)
[18] Pettersson, S., & Lennartson, B. (2001). Stabilization of hybrid systems using a min-projection strategy. Proceedings of the American control conference (pp. 223-228).
[19] Prajna, S., & Papachristodoulou, A. (2003). Analysis of switched and hybrid systems--beyond piecewise quadratic methods. Proceedings of the American control conference (pp. 2779-2784).
[20] Wicks, M. A., Peleties, P., & DeCarlo, R. A. (1994). Construction of piecewise Lyapunov functions for stabilizing switched systems. Proceedings of the 33rd IEEE conference on decision control (pp. 3492-3497).
[21] Wu, F.: A generalized LPV system analysis and control synthesis framework. International journal of control 74, No. 7, 745-759 (2001) · Zbl 1011.93046
[22] Wu, F.; Yang, X. H.; Packard, A.; Becker, G.: Induced L2 norm control for LPV systems with bounded parameter variation rates. International journal of robust nonlinear control 6, No. 9/10, 983-998 (1996) · Zbl 0863.93074
[23] Ye, H.; Michel, A. N.; Hou, L.: Stability theory for hybrid dynamical systems. IEEE transactions on automatic control 43, No. 4, 461-474 (1998) · Zbl 0905.93024