Input–output-to-state stability for discrete-time systems

This paper presents Lyapunov characterizations of uniform output-to-state stability and uniform input–output-to-state stability (IOSS) (with respect to disturbances) for discrete-time (DT) nonlinear systems. We show the equivalence of the following three properties for DT systems: uniform IOSS, exis...

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Published in	Automatica (Oxford) Vol. 44; no. 2; pp. 326 - 336
Main Authors	Cai, Chaohong, Teel, Andrew R.
Format	Journal Article
Language	English
Published	Oxford Elsevier Ltd 01.02.2008 Elsevier
Subjects	Applied sciences Computer science; control theory; systems Control system analysis Control theory. Systems Discrete-time systems Exact sciences and technology Lyapunov functions Modelling and identification Norm estimators Stability Discrete-time systems Stability Lyapunov functions Norm estimators Non linear control Optimization Input to state stability Smooth function Observer Discrete time System identification State estimation Lyapunov function
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ISSN	0005-1098 1873-2836
DOI	10.1016/j.automatica.2007.05.022

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Abstract	This paper presents Lyapunov characterizations of uniform output-to-state stability and uniform input–output-to-state stability (IOSS) (with respect to disturbances) for discrete-time (DT) nonlinear systems. We show the equivalence of the following three properties for DT systems: uniform IOSS, existence of a smooth Lyapunov function for uniform IOSS, and existence of a (state-)norm estimator. This equivalence result is a DT counterpart of Krichman et al. [2001. Input–output-to-state stability. SIAM Journal on Control and Optimization 39, 1874–1928. Theorem 2.4] and a generalization of Jiang and Wang [2002. A converse Lyapunov theorem for discrete-time systems with disturbances. Systems and Control Letters 45, 49–58. Theorem 1.1] and Jiand and Wang [2001. Input-to-state stability for discrete-time nonlinear systems. Automatica 37, 857–869. Theorem 1, 1 ⇔ 4 ].
AbstractList	This paper presents Lyapunov characterizations of uniform output-to-state stability and uniform input–output-to-state stability (IOSS) (with respect to disturbances) for discrete-time (DT) nonlinear systems. We show the equivalence of the following three properties for DT systems: uniform IOSS, existence of a smooth Lyapunov function for uniform IOSS, and existence of a (state-)norm estimator. This equivalence result is a DT counterpart of Krichman et al. [2001. Input–output-to-state stability. SIAM Journal on Control and Optimization 39, 1874–1928. Theorem 2.4] and a generalization of Jiang and Wang [2002. A converse Lyapunov theorem for discrete-time systems with disturbances. Systems and Control Letters 45, 49–58. Theorem 1.1] and Jiand and Wang [2001. Input-to-state stability for discrete-time nonlinear systems. Automatica 37, 857–869. Theorem 1, 1 ⇔ 4 ].
Author	Cai, Chaohong Teel, Andrew R.
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Keywords	Discrete-time systems Stability Lyapunov functions Norm estimators Non linear control Optimization Input to state stability Smooth function Observer Discrete time System identification State estimation Lyapunov function
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SubjectTerms	Applied sciences Computer science; control theory; systems Control system analysis Control theory. Systems Discrete-time systems Exact sciences and technology Lyapunov functions Modelling and identification Norm estimators Stability
Title	Input–output-to-state stability for discrete-time systems
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