The concept of ‘exponential input to state stability’ for stochastic systems and applications to feedback stabilization. (English) Zbl 0913.93067

Summary: This paper presents a version of Sontag’s well-known ‘input-to-state-stability’ property for stochastic systems. This concept is used to derive sufficient conditions for global stabilization for a certain class of stochastic nonlinear systems by means of static and dynamic output feedback.


93D25 Input-output approaches in control theory
93E15 Stochastic stability in control theory
93C10 Nonlinear systems in control theory
93B52 Feedback control
93D15 Stabilization of systems by feedback
Full Text: DOI


[1] L. Arnold, Stochastic Differential Equations, Theory and Applications, Wiley, New York, 1974. · Zbl 0278.60039
[2] Coron, J.M.; Praly, L., Adding an integrator for the stabilization problem, Systems and control lett., 17, 89-104, (1991) · Zbl 0747.93072
[3] H. Deng, M. Krstic, Stochastic nonlinear stabilization – part I: a backstepping design, submitted. · Zbl 0902.93049
[4] H. Deng, M. Krstic, Stochastic nonlinear stabilization - Part II: inverse optimality, submitted. · Zbl 0902.93050
[5] H. Deng, M. Krstic, Output-feedback stochastic nonlinear stabilization, submitted. · Zbl 0958.93095
[6] Florchinger, P., Lyapunov-like techniques for stochastic stability, SIAM J. control opt., 33, 1151-1169, (1995) · Zbl 0845.93085
[7] P. Florchinger, E.I. Verriest, Applications of stochastic Artstein’s theorem to feedback stabilization, Proc. NOLCOS 95, 1995, pp. 837-841.
[8] Jiang, Z.P.; Teel, A.; Praly, L., Small-gain theorem for ISS systems and applications, Math. control signals systems, 7, 95-120, (1994) · Zbl 0836.93054
[9] P.E. Kopp, Martingales and Stochastic Integrals, Cambridge University Press, Cambridge, MA, 1983.
[10] Mao, X., Exponential stability of large-scale stochastic differential equations, Systems control lett., 19, 71-82, (1992)
[11] Mao, X., Stochastic stabilization and destabilization, Systems control lett., 23, 279-290, (1994) · Zbl 0820.93071
[12] Sontag, E.D., A universal construction of artstein’s theorem on nonlinear stabilization, Systems control lett., 13, 117-123, (1989) · Zbl 0684.93063
[13] Sontag, E.D., Smooth stabilization implies coprime factorization, IEEE trans. automat. control, 34, 435-443, (1989) · Zbl 0682.93045
[14] Sontag, E.D.; Wang, Y., On characterizations of the input-to-state stability property, Systems control lett., 24, 351-359, (1995) · Zbl 0877.93121
[15] Sontag, E.D.; Wang, Y., Output-to state stability and detectability of nonlinear systems, Systems control lett., 29, 279-290, (1997) · Zbl 0901.93062
[16] J. Tsinias, A theorem on global stabilizable of nonlinear systems by linear feedback, Systems Control Lett. 17 (1991) 357-362. · Zbl 0749.93071
[17] J. Tsinias, Output feedback global stabilization for triangular systems, Proc. NOLCOS 95, 1995, pp. 238-243.
[18] J. Tsinias, Versions of Sontag’s input to state stability condition and output feedback global stabilization, J. Math. Estimation Control 6 (1996) 113-116 (Summary). · Zbl 0844.93068
[19] J. Tsinias, Input to state stability properties of nonlinear systems and applications to bounded feedback stabilization using saturation, COCV-ESAIM 2 (1997) 57-85. · Zbl 0871.93047
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.