A generalized homogeneous domination approach for global stabilization of inherently nonlinear systems via output feedback. (English) Zbl 1113.93087

Polendo, Jason; Qian, Chunjiang

Int. J. Robust Nonlinear Control 17, No. 7, 605-629 (2007).

Summary: We introduce a generalized framework for global output feedback stabilization of a class of uncertain, inherently nonlinear systems of a particularly complex nature since their linearization around the equilibrium is not guaranteed to be either controllable or observable. Based on a new observer/controller construction and a homogeneous domination design, this framework not only unifies the existing output feedback stabilization results, but also leads to more general results which have been never achieved before, establishing this methodology as a universal tool for the global output feedback stabilization of inherently nonlinear systems.

MSC:

93D15	Stabilization of systems by feedback
93B52	Feedback control
93C10	Nonlinear systems in control theory
93C41	Control/observation systems with incomplete information

Keywords:

homogeneous domination approach; global output feedback stabilization; inherently nonlinear systems

References:

[1]	Mazenc, Systems and Control Letters 23 pp 119– (1994)
[2]	Bestle, International Journal of Control 38 pp 419– (1983)
[3]	Krener, Systems and Control Letters 3 pp 47– (1983)
[4]	Krener, SIAM Journal on Control Optimization 23 pp 197– (1985)
[5]	Krener, SIAM Journal on Control Optimization 41 pp 932– (2002)
[6]	Marino, Systems and Control Letters 17 pp 115– (1991)
[7]	Besancon, NOLCOS 2 pp 399– (1998)
[8]	. Global output feedback stabilization for uncertain nonlinear systems with output dependent incremental rate. Proceedings of 2004 American Control Conference, Boston, MA, 2004; 3047–3052.
[9]	Gauthier, IEEE Transactions on Automatic Control 37 pp 875– (1992)
[10]	Khalil, IEEE Transactions on Automatic Control 32 pp 1031– (1987)
[11]	Qian, IEEE Transactions on Automatic Control 47 pp 2068– (2002)
[12]	Tsinias, Systems and Control Letters 17 pp 357– (1991) · Zbl 0749.93071
[13]	Yang, International Journal on Robust and Nonlinear Control 15 pp 247– (2005)
[14]	Qian, IEEE Transactions on Automatic Control 47 pp 1710– (2002)
[15]	A homogeneous domination approach for global output feedback stabilization of a class of nonlinear systems. Proceedings of 2005 American Control Conference, Portland, OR, June 2005; 4708–4715. Also under revision in IEEE Transactions on Automatic Control.
[16]	Qian, IEEE Transactions on Automatic Control 46 pp 1061– (2001)
[17]	Yang, IEEE Transactions on Automatic Control 50 pp 619– (2005)
[18]	Qian, IEEE Transactions on Automatic Control 51 pp 1457– (2006)
[19]	. Liapunov Functions and Stability in Control Theory. Lecture Notes in Control and Information Sciences, vol. 267. Springer: Berlin, 2001. · Zbl 0968.93004
[20]	Homogeneous coordinates and continuous asymptotically stabilizing feedback controls. Differential Equations (Colorado Springs, CO, 1989). Lecture Notes in Pure and Applied Mathematics, vol. 127. Dekker: New York, 1991; 249–260.
[21]	Dayawansa, SIAM Journal on Control Optimization 28 pp 1321– (1990)
[22]	Recent advances in the stabilization problem for low dimensional systems. Proceeding of 1992 IFAC NOLCOS, Bordeaux, France, 1992; 1–8.
[23]	Kawski, Control Theory and Advanced Technology 6 pp 497– (1990)