A Strict ISS-Lyapunov Function for LTV Systems With Non-Time-Differentiable Dynamics

We study stability and robustness for a large class of linear time-varying systems under the assumption that the system possesses some kind of excitation that ensures uniform attractivity of the origin, but not even boundedness of the solutions is assumed a priori. Our main statements provide strict Lyapunov functions, i.e., having a strictly negative-definite derivative, constructed based on an initial candidate whose derivative is sign undefined. The Lyapunov function that we construct guarantees uniform global asymptotic stability and input-to-state stability with respect to bounded additive inputs. As a byproduct of our main results, we provide a Lyapunov function for a class of systems reminiscent of model-reference adaptive control with non-differentiable regressors.