Robust adaptive regulation of linear time-varying systems

Given reference signals generated by a stable, linear time-invariant exosystem, to be tracked by the output, the problem of robust adaptive regulation by output feedback is addressed for single-input, single-output linear systems with unknown time-varying parameters and unmodeled bounded additive disturbances. Without requiring parameters or disturbances to be slowly varying or to have known bounds, a robust adaptive regulator is designed that ensures boundedness of closed-loop signals and arbitrarily improved transient performance for the regulation error. Asymptotic regulation is achieved when parameters belong to a compact set determined by the controller parameters' time derivatives are L₁∩L_∞, and disturbances and parameter variations from unknown constant nominal values are L₂∩L_∞