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.
Reviewer: V.Răsvan (Craiova)
References:
| [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, (PhD thesis (1993), École des Mines de Paris) |
| [4] | Jiang, Z. P.; Mareels, I. M.Y., Robust control of time-varying nonlinear cascaded systems with dynamic uncertainties, (Proc. European Control Conf. (ECC’95). Proc. European Control Conf. (ECC’95), Rome (1995)), 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, (Preprints IFAC Nonlinear Control Systems Design Symp. (NOLCOS ’95). Preprints IFAC Nonlinear Control Systems Design Symp. (NOLCOS ’95), Tahoe City, CA (1995)), 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 |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
