Fixed-Time Stabilization of Uncertain Continuous-Time Systems With Sampled Control

We prove fixed time stabilization estimates using sampled controls, for continuous-time time-varying linear systems that can contain uncertain coefficient matrices. In the special case where the coefficient matrices are known, this yields a fixed-time input-to-state stability property, in which the norm of the current state is bounded from above by a supremum of the uncertainty that is calculated over a finite length time interval of a constant length. We also prove analogs for output feedback stabilization with unknown measurement delays, and for nonlinear systems with state delays and outputs. We illustrate our work using a pendulum dynamics with an unknown control gain and poorly known friction.