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A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems. (English) Zbl 0857.93089
Small gain theorems are studied for interconnected systems of the form \[ \dot x_1=f_1(x_1,x_2,u_1), \qquad \dot x_2=f_2(x_1,x_2,u_2) \] using smooth Lyapunov functions for the component systems.

93D30 Lyapunov and storage functions
93C10 Nonlinear systems in control theory
Full Text: DOI
[1] Grujić, L.T.; Šiljak, D.D., Asymptotic stability and instability of large-scale systems, IEEE trans. autom. control, AC-18, 636-645, (1973) · Zbl 0279.93031
[2] Hill, D.J., A generalization of the small-gain theorem for nonlinear feedback systems, Automatica, 27, 1047-1050, (1991)
[3] Jiang, Z.P., Quelques résultats de stabilisation robuste. application à la commande, ()
[4] Jiang, Z.P.; Mareels, I.M.Y., Robust control of time-varying nonlinear cascaded systems with dynamic uncertainties, (), 659-664
[5] Jiang, Z.P.; Teel, A.; Praly, L., Small-gain theorem for ISS systems and applications, Math. control, sig., syst., 7, 95-120, (1994) · Zbl 0836.93054
[6] Lin, Y.; Sontag, E.D.; Wang, Y., A smooth converse Lyapunov theorem for robust stability, SIAM J. control optim., 34, 124-160, (1996) · Zbl 0856.93070
[7] Mareels, I.M.Y.; Hill, D.J., Monotone stability of nonlinear feedback systems, J. math. syst. estim. control, 2, 275-291, (1992) · Zbl 0776.93039
[8] Praly, L.; Jiang, Z.P., Stabilization by output feedback for systems with ISS inverse dynamics, Syst. control lett., 21, 19-34, (1993) · Zbl 0784.93088
[9] Praly, L.; Wang, Y., Stabilization in spite of matched unmodelled dynamics and an equivalent definition of input-to-state stability, Math. control, sig. syst., (1996), to appear · Zbl 0869.93040
[10] Sontag, E.D., Smooth stabilization implies coprime factorization, IEEE trans. autom. control, AC-34, 435-443, (1989) · Zbl 0682.93045
[11] Sontag, E.D., Further facts about input to state stabilization, IEEE trans. autom. control, AC-35, 473-476, (1990) · Zbl 0704.93056
[12] Sontag, E.D., On the input-to-state stability property, Eur. J. control, 1, 24-36, (1995) · Zbl 1177.93003
[13] Sontag, E.D.; Teel, A., Changing supply functions in input/state stable systems, IEEE trans. autom. control, AC-40, 1476-1478, (1995) · Zbl 0832.93047
[14] Sontag, E.D.; Wang, Y., On characterizations of the input-to-state stability property, Syst. control lett., 24, 351-359, (1995) · Zbl 0877.93121
[15] Sontag, E.D.; Wang, Y., On characterizations of set input-to-state stability, (), 226-231
[16] Teel, A.; Praly, L., Tools for semi-global stabilization by partial state and output feedback, SIAM J. control optim., (1996), to appear
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