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Output feedback global stabilization for a class of nonlinear systems with unmodelled dynamics. (English) Zbl 0862.93050
The authors consider a single-input, single-output minimum phase linear plant \[ \dot x=Fx+gu+\mu h_1g+h_2,\quad y=cx.\tag{1} \] The relative degree may be greater than 1. The system is connected with two nonlinear systems \[ \dot\xi=q_1(\xi,u),\quad h_1=\psi(\xi,u)\tag{2} \] and \[ \dot\zeta=q_2(\zeta,y),\quad h_2=\phi(y,\zeta)\tag{3} \] whose dynamics are in general unmodeled. However, it is required that (2) has a linear structure (with an unknown Hurwitz matrix) and that the input/output behaviour of (3) satisfies suitable assumptions (in particular, the input/output gain is assumed to be known). The main contribution is an existence result for output dynamic feedback of the form \(\dot\chi=\varphi(y,\chi)\), \(u=\theta(y,\chi)\) which stabilizes the system for all the sufficiently small values of \(\mu\).

93D21 Adaptive or robust stabilization
93C10 Nonlinear systems in control theory
93C41 Control/observation systems with incomplete information
Full Text: DOI
[1] Jiang, Z.P.; Teel, A.; Praly, L., Small-gain theorem for ISS systems and applications, Mathematics of control, signals and systems, 7, 95-120, (1994) · Zbl 0836.93054
[2] Sontag, E.D., Smooth stabilization implies coprime factorization, IEEE trans automat control, 34, 435-443, (1989) · Zbl 0682.93045
[3] Krener, A.J.; Isidori, A., Linearization by output injection and nonlinear observers, Systems & control letters, 3, 47-52, (1983) · Zbl 0524.93030
[4] Marino, R.; Tomei, P., Dynamic output feedback linearlization and global stabilization, Systems & control letters, 17, 115-121, (1991) · Zbl 0747.93069
[5] Marino, R.; Tomei, P., Global adaptive output-feedback control of nonlinear systems, Parts I and II. IEEE trans automat contr, 38, 17-48, (1993) · Zbl 0799.93023
[6] Kanellakopoulos, I.; Kokotović, P.V.; Morse, A.S., A toolkit for nonlinear feedback design, Systems & control letters, 18, 83-92, (1992) · Zbl 0743.93039
[7] Praly, L.; Jiang, Z.P., Stabilization by output feedback for systems with ISS inverse dynamics, Systems & control letters, 21, 19-33, (1993) · Zbl 0784.93088
[8] Teel, A.; Praly, L., On output-feedback stabilization for systems with ISS inverse dynamics and uncertainties, (), 1942-1947
[9] Krstić, M.; Sun, J.; Kokotović, P.V., Robust control of strict- and output-feedback systems with input unmodelled dynamics, (), 2257-2262
[10] Jiang ZP, Pomet J-B. A note on’robust control of nonlinear systems with input unmodelled dynamics’. Technical Report, INRIA, no. 2293, June 1994
[11] Qu, Z., Model reference robust control of SISO systems with significant unmodelled dynamics, (), 255-259
[12] Mareels, I.M.Y.; Hill, O.J., Monotone stability of nonlinear feedback systems, J math systems estimation control, 2, 275-291, (1992) · Zbl 0776.93039
[13] Sontag, E.D., On the input to state stability property, Eur J of control, 1, 24-36, (1995) · Zbl 1177.93003
[14] Desoer, C.; Vidyasagar, M., Feedback systems: inputoutput properties, (1975), Academic Press New York. · Zbl 0327.93009
[15] Sannuti, P.; Saberi, A., Special coordinate basis for multivariable linear systems-finite and infinite zero structure, squaring down and decoupling, Int J control, 45, 1655-1704, (1987) · Zbl 0623.93014
[16] Spong, M.W.; Vidyasagar, M., Robot dynamics and control, (1989), John Wiley New York
[17] Jiang, Z.P.; Mareels, I.M.Y., Robust control of time-varying nonlinear cascaded systems with dynamic uncertainties, (), p659-p664
[18] Jiang ZP. Quelques résultats de stabilisation robuste. Applications à la commande. Thèse de l’Ecole des Mines de Paris. 1993
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