Robust adaptive regulation of linear time-varying systems

Given reference signals generated by a stable, linear time-invariant exosystem, we address the problem of robust adaptive regulation for linear systems with unknown time-varying parameters and disturbances. We show how to design a robust adaptive regulator without requiring the parameters to be slowly time-varying or to have known bounds, while ensuring arbitrarily improved transient performance for the regulation error. Asymptotic regulation is achieved when parameters belong to a given compact set, disturbances are L₂∩L_∞ signals and parameter time derivatives are L₁∩L_∞ signals