Ripple-free robust output regulation and tracking for multirate sampled-data control systems

The problem of the robust continuous-time asymptotic tracking and disturbance rejection for a multivariable multirate sampled-data system is studied. The necessity of a continuous-time internal model of the exogenous signals (except for the constant ones, if any) for obtaining a ripple-free zero error response, is proven. The conditions are given for the existence of a hybrid control system (including, possibly, a continuous-time subcompensator) for which the exponential stability and a continuous-time convergence to zero of the tracking error are guaranteed at least in a neighbourhood of the nominal parameters. This, in particular, both for when the dead-beat convergence of the state free response and the continuous-time error response is required at the nominal parameters, and for when an exponential convergence with a prescribed rate of decay is required (including design procedures of the continuous-time and the discrete-time subcompensators); both for when the available description of the plant has a known dependence on some 'physical' parameters, and for when the only nominal description of the plant is available, and independent perturbations of the entries of (some of) the matrices characterizing the plant representation are assumed.