Variable structure robust controller for linear time-varying systems with disturbances

A variable structure robust controller is given for single-input and single-output linear time-varying systems with disturbances. Time-varying parameters are not restricted to be either slow time-varying or of known structure. Here only the smooth condition and boundedness of system parameters are required. By introducing some auxiliary signals and normalized signals with memory functions and appropriate choice of controller parameters, the proposed variable structure robust control scheme guarantees the uniform boundedness of all signals in the closed-loop system and the convergence of the tracking error to stay in an arbitrarily small compact set.