On characterizations of the input-to-state stability property
Systems & Control Letters
Linear system theory (2nd ed.)
Linear system theory (2nd ed.)
A Smooth Converse Lyapunov Theorem for Robust Stability
SIAM Journal on Control and Optimization
Output-to-state stability and detectability of nonlinear systems
Systems & Control Letters
Nonlinear Control Systems II
Input-Output-to-State Stability
SIAM Journal on Control and Optimization
Lyapunov Characterizations of Input to Output Stability
SIAM Journal on Control and Optimization
Separation Principles for Input-Output and Integral-Input-to-State Stability
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Input-to-state stability for discrete-time nonlinear systems
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Hi-index | 22.14 |
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].