On characterizations of the input-to-state stability property. (English) Zbl 0877.93121

Summary: We show that the well-known Lyapunov sufficient condition for “input-to-state stability” (ISS) is also necessary, settling positively an open question raised by several authors during the past few years. Additional characterizations of the ISS property, including one in terms of nonlinear stability margins, are also provided.


93D25 Input-output approaches in control theory
93C10 Nonlinear systems in control theory
Full Text: DOI


[2] Lin, Y.; Sontag, E. D.; Wang, Y., A smooth converse Lyapunov theorem for robust stability, (IMA Preprint # 1192 (1993), Institute for Mathematics and Its Applications, University of Minnesota), submitted. See also · Zbl 0856.93070
[3] Praly, L.; Jiang, Z.-P., Stabilization by output feedback for systems with ISS inverse dynamics, Systems Control Lett., 21, 19-34 (1993) · Zbl 0784.93088
[4] Sontag, E. D., Smooth stabilization implies coprime factorization, IEEE Trans. Automat. Control, AC-34, 435-443 (1989) · Zbl 0682.93045
[5] Sontag, E. D., Some connections between stabilization and factorization, (Proc. IEEE Conf. Decision and Control. Proc. IEEE Conf. Decision and Control, Tampa (1989)), 990-995
[6] Sontag, E. D., Further facts about input to state stabilization, IEEE Trans. Automat. Control, AC-35, 473-476 (1990) · Zbl 0704.93056
[7] Tsinias, J., Sontag’s “input to state stability condition” and global stabilization using state detection, Systems Control Lett., 20, 219-226 (1993) · Zbl 0768.93063
[8] Tsinias, J., Versions of Sontag’s input to state stability condition and the global stabilizability problem, SIAM J. Control Optim., 31, 928-941 (1993) · Zbl 0788.93076
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.