Converse Lyapunov Theorems for Discrete-Time Systems : an Alternative Approach

This paper presents an alternative approach for obtaining a converse Lyapunov theorem for discrete-time systems. The proposed approach is constructive, as it provides an explicit Lyapunov function. The developed converse Lyapunov theorem establishes existence of global Lyapunov functions for globally exponentially stable (GES) systems and for globally asymptotically stable systems, Lyapunov functions on a set [a, b] ⊂ R+ are derived. In particular, we discuss our result for both continuous and discontinuous dynamics. keyword: Discrete-time systems, Stability analysis, Converse Lyapunov theorems

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