Further results on Lyapunov functions for slowly time-varying systems
We provide general methods for explicitly constructing strict Lyapunov functions for fully nonlinear slowly time-varying systems. Our results apply to cases where the given dynamics and corresponding frozen dynamics are not necessarily exponentially stable. This complements our previous Lyapunov function constructions for rapidly time-varying dynamics. We also explicitly construct input-to-state stable Lyapunov functions for slowly time-varying control systems. We illustrate our findings by constructing explicit Lyapunov functions for a pendulum model, an example from identification theory, and a perturbed friction model. © Springer-Verlag London Limited 2006.
Publication Source (Journal or Book title)
Mathematics of Control, Signals, and Systems
Mazenc, F., & Malisoff, M. (2007). Further results on Lyapunov functions for slowly time-varying systems. Mathematics of Control, Signals, and Systems, 19 (1), 1-21. https://doi.org/10.1007/s00498-006-0010-4