A converse Lyapunov theorem for discrete-time systems with disturbances

By Zhong-Ping Jiang, Yuan Wang. Systems & control letters (Print), 2002

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The Liapunov's second method for continuous time difference equations (2003, methodology): “Maybe the transformation of continuous time difference equations into infinite dimensional discrete time systems could be useful for suitably extending the results of the paper [16] to the systems here studied.”
Closed-Loop Inverse Kinematics for Redundant Robots: Comparative Assessment and Two Enhancements (2015, background): “Although there exist discretetime versions of it [30], their application is not immediate, and some additional assumptions must be made.”
Rapidly Exponentially Stabilizing Control Lyapunov Functions and Hybrid Zero Dynamics (2014, background): “Definition 1: (Based on [9] for continuous-time systems and [25], [56] for discrete-time systems.”
Provably safe and robust learning-based model predictive control (2011, methodology): “In particular, we can design O n to be a statistical tool that identiﬁes better system models.”
Classical Converse Theorems in Lyapunov's Second Method (2015, background): “A converse theorem for strong uniform global asymptotic stability of a difference inclusion was provided by Jiang and Wang [36].”