×

zbMATH — the first resource for mathematics

State feedback design for input-saturating quadratic systems. (English) Zbl 1194.93185
Summary: This paper proposes a method to design stabilizing state feedback control laws for nonlinear quadratic systems subject to input saturation. Based on a quadratic Lyapunov function, a modified sector condition and a particular representation for the quadratic terms, synthesis conditions in a “quasi”-LMI form are stated in a regional (local) context. An LMI-based optimization problem is then derived for computing the state feedback gains maximizing the estimate of the stability region of the closed-loop system.

MSC:
93D15 Stabilization of systems by feedback
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Amato, F., Ambrosino, R., Ariola, M., Consentino, C., & Merola, A. (2007). State feedback control of nonlinear quadratic systems. In Proceedings of the 47th conference on decision and control, CDC’07, New Orleans, USA.
[2] Amato, F.; Consentino, C.; Merola, A., On the region of attraction of nonlinear quadratic systems, Automatica, 43, 2119-2123, (2007) · Zbl 1138.93028
[3] Bernstein, D.S., A plant taxonomy for designing control experiments, IEEE control systems magazine, 7-14, (2001)
[4] Blanchini, F., Set invariance in control, Automatica, 35, 1747-1767, (1999) · Zbl 0935.93005
[5] Chesi, G., Computing output feedback controllers to enlarge the domain of attraction in polynomial systems, IEEE transactions on automatic control, 49, 10, 1846-1850, (2004) · Zbl 1365.93204
[6] Chesi, G.; Garulli, A.; Tesi, A.; Vicino, A., LMI-based computation of optimal quadratic Lyapunov functions for odd polynomial systems, International journal of robust and nonlinear control, 15, 35-49, (2005) · Zbl 1056.93059
[7] de Klerk, E., Aspects of semidefinite programming. interior point algorithms and selected applications, (2002), Kluwer Dordrecht, The Netherlands · Zbl 0991.90098
[8] Genesio, R.; Tartaglia, M.; Vicino, A., On the estimation of asymptotic stability regions: state of the art and new proposals, IEEE transactions on automatic control, 30, 8, 747-755, (1985) · Zbl 0568.93054
[9] Hu, T.; Lin, Z., Control systems with actuator saturation: analysis and design, (2001), Birkhäuser Boston · Zbl 1061.93003
[10] ()
[11] Khalil, H.K., Nonlinear systems, (2002), Prentice Hall London, pp. 312-322
[12] Koditschek, D.E.; Narendra, K.S., The stability of second-order quadratic differential equations, IEEE transactions on automatic control, 27, 4, 783-798, (1982) · Zbl 0498.93044
[13] Robinson, C., Dynamical systems: stability, symbolic dynamics and chaos, (1998), CRC, pp. 344-346
[14] Sarkar, R.R.; Banerjee, S., Cancer self remission and tumor stability—a stochastic approach, Mathematical biosciences, 196, 1, 65-81, (2005) · Zbl 1071.92017
[15] ()
[16] Tarbouriech, S.; Prieur, C.; Gomes da Silva, J.M., Stability analysis and stabilization of systems presenting nested saturations, IEEE transactions on automatic control, 51, 8, 1364-1371, (2006) · Zbl 1366.93531
[17] Thapar, J.; Vittal, V.; Kliemann, W.; Fouad, A.A., Application of the normal form of vector fields to predict inter-area separation in power systems, IEEE transactions on power systems, 12, 2, 844-850, (1997)
[18] Valmórbida, G., Tarbouriech, S., & Garcia, G. (2009). State feedback design for input-saturating nonlinear quadratic systems. In Proceedings of the 2009 American control conference.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.