| Lyapunov Function Constructions for Slowly Time-Varying Systems (2008) | |||||||||||||||
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| Abstract — 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-tostate stable Lyapunov functions for slowly time-varying control systems. We illustrate our findings using a perturbed friction model with slowly time-varying coefficients. Index Terms—Lyapunov function constructions, slowly timevarying systems, stability analysis, input-to-state stability I. | |||||||||||||||
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