Lyapunov Function Constructions for Slowly Time-Varying Systems

We provide general methods for explicitly constructing strict Lyapunov functions for general nonlinear slowly time-varying non-autonomous 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 using a perturbed friction model with slowly time-varying coefficients

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