Global stabilizability and observability imply semi-global stabilizability by output feedback. (English) Zbl 0820.93054

Teel, Andrew; Praly, Laurent

Syst. Control Lett. 22, No. 5, 313-325 (1994).

Nonlinear, continuous, finite-dimensional dynamical systems are considered. It is proved, that smooth global stabilizability and complete uniform observability are sufficient properties for semi-global output feedback stabilizability. The design procedure for a dynamic output feedback is presented. The proofs of the theorems are based on the concept of Lyapunov function. Moreover, some remarks and comments on the relationships between observability and different types of stabilizability are given. The results presented in the paper are connected with the methods given in [A. Tornambé, “Output feedback stabilization of a class of non-minimum phase nonlinear systems”, Syst. Control Lett. 19, No. 3, 193-204 (1992; Zbl 0763.93075)].

Reviewer: J.Klamka (Katowice)

MSC:

93D15	Stabilization of systems by feedback
93B07	Observability
93C15	Control/observation systems governed by ordinary differential equations
93C10	Nonlinear systems in control theory

Keywords:

nonlinear; global stabilizability; observability; output feedback stabilizability; dynamic output feedback; Lyapunov function

References:

[1]	Bacciotti, A., Linear feedback: the local and potentially global stabilization of cascade systems, (), 21-25
[2]	Byrnes, C.I.; Isidori, A., New results and examples in nonlinear feedback stabilization, Systems control lett., 12, 437-442, (1989) · Zbl 0684.93059
[3]	Gauthier, J.-P.; Bornard, G., Observability for any u(t) of a class of nonlinear systems, IEEE trans. automat. control, 26, 922-926, (1981) · Zbl 0553.93014
[4]	Kanellakopoulos, I.; Kokotovic, P.V.; Morse, A.S., A toolkit for nonlinear feedback design, Systems control lett., 18, 83-92, (1992) · Zbl 0743.93039
[5]	Khalil, H.K.; Esfandiari, F., Semi-global stabilization of a class of nonlinear systems using output feedback, (), 3423-3428
[6]	Kurzweil, J., On the inversion of Lyapunov’s second theorem on stability of motion, Amer. math. soc. transl. ser. 2, 24, 19-77, (1956)
[7]	Marino, R.; Tomei, P., Dynamic output feedback linearization and global stabilization, Systems control lett., 17, 115-121, (1991) · Zbl 0747.93069
[8]	F. Mazenc, L. Praly and W.P. Dayawansa, Global stabilization by output feedback: examples and counter-examples, Systems Control Lett., submitted. · Zbl 0816.93068
[9]	J.-B. Pomet, R.M. Hirschorn and W.A. Cebuhar, Dynamic output feedback regulation for a class of nonlinear systems, Math. Control Signals Systems, to appear. · Zbl 0792.93048
[10]	Praly, L., Lyapunov design of a dynamic output feedback for system linear in their unmeasured state components, (), 31-36
[11]	L. Praly and Z.P. Jiang, Stabilization by output feedback for systems with its inverse dynamics, Systems Control Lett., to appear. · Zbl 0784.93088
[12]	Sontag, E.D., Conditions for abstract nonlinear regulation, Inform. and control, 51, 105-127, (1981) · Zbl 0544.93058
[13]	A.R. Teel and L. Praly, Tools for semi-global stabilization by partial state and output feedback, SIAM J. Control Optim., submitted. · Zbl 0843.93057
[14]	Tornambé, A., Output feedback stabilization of a class of non-minimum phase nonlinear systems, Systems control lett., 19, 193-204, (1992) · Zbl 0763.93075
[15]	Tsinias, J., Sufficient Lyapunov-like conditions for stabilization, Math. control signals systems, 2, 343-357, (1989) · Zbl 0688.93048
[16]	Tsinias, J., A generalization of Vidyasagar’s theorem on stabilizability using state detection, Systems control lett., 17, 37-42, (1991) · Zbl 0753.93063