zbMATH — the first resource for mathematics

Some results on global and semiglobal stabilization of affine-systems. (English) Zbl 0902.93053
Summary: The relations between semiglobal stabilization and global stabilization of affine systems are investigated. It is shown that for one-dimensional systems the two concepts are equivalent. For the $$n$$-dimensional case we introduce a more restrictive concept, the $$L$$-semiglobal stabilization, which implies global stabilization. This result is applied to bilinear systems.

MSC:
 93D15 Stabilization of systems by feedback 93C10 Nonlinear systems in control theory
Full Text:
References:
 [1] V. Andriano, Stabilitàe stabilizzabilità dei sistemi non lineari: aspetti locali, globali e applicazioni, Tesi di Dottorato, 1995. [2] Artstein, Z., Stabilization with relaxed controls,, Nonlinear anal. TMA, 7, 1163-1173, (1983) · Zbl 0525.93053 [3] A. Bacciotti, Potentially global stabilizability, IEEE Trans. Automat. Control AC-31 (10) (1986). · Zbl 0605.93043 [4] A. Bacciotti, Linear feedback: the local and potentially global stabilization of cascade systems, IFAC Conf., Nolcos, 1992. [5] Bacciotti, A., The potentially global stabilization property of certain planar systems,, Appl. math. lett., 6(2), 75-78, (1993) · Zbl 0773.93072 [6] C.I. Byrnes, A. Isidori, Global feedback stabilization of nonlinear systems, Proc. 24th Conf. on Decision and Control, Fl. Lauderdale, December 1985, pp. 1031-1037. [7] C.I. Byrnes, A. Isidori, Asymptotic stabilization of minimum phase nonlinear systems, IEEE Trans. Automat. Control 36(10) (1991). · Zbl 0758.93060 [8] Hammouri, H.; Marques, J.C., Stabilization of homogeneous bilinear systems,, Appl. math. lett., 7(1), 23-28, (1994) · Zbl 0797.93039 [9] Isidori, A., Global almost disturbance decoupling with stability for non minium-phase single-input single-output nonlinear systems,, Systems control lett., 28, 115-122, (1996) · Zbl 0877.93055 [10] J.L. Massera, Contributions to stability theory, Ann. Math. 64(1) (1956). · Zbl 0070.31003 [11] Ortega, R., Passivity properties for stabilization of cascaded nonlinear systems,, Automatica, 27(2), 423-424, (1991) · Zbl 0729.93065 [12] P. Seibert, R. Suarez, Global stabilization of nonlinear cascade systems, Systems Control Lett. 14 (1990). · Zbl 0699.93073 [13] Sontag, E.D., A ‘universal’ construction of artstein’s theorem on nonlinear stabilization,, Systems control lett., 13, 117-123, (1989) · Zbl 0684.93063 [14] E.D. Sontag, Feedback stabilization of nonlinear systems, in: A. Kaashoek, J.H. van Schuppen, A.C.M. Ran (Eds.), Robust Control of Linear Systems and Nonlinear Control, Birkhauser, Boston, 1990. · Zbl 0735.93063 [15] Sussmann, H.J.; Kokotovic, P.V., The peaking phenomenon and the global stabilization of nonlinear systems,, IEEE trans. automat. control, 36(4), 424-440, (1991) · Zbl 0749.93070 [16] Teel, A.; Praly, L., Tools for semiglobal stabilization by partial state and output feedback,, SIAM J. control optim., 33(5), 1443-1488, (1995) · Zbl 0843.93057
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.