Continuous-time asymptotic tracking and regulation for parameter-dependent multi-rate sampled-data systems

The robust ripple-free tracking and regulation problem, in the presence of reference and disturbance signals of sinusoidal-exponential kind, is solved for multi-rate sampled-data systems, whose state-space description is assumed to depend on some unknown “physical” parameters. Making use of a hybrid control system, including a continuous-time internal model of the exogenous signals and a periodic discrete-time subcompensator, continuous-time exponential convergence with a prescribed rate of decay is obtained for the error response, at least in a neighbourhood of the nominal parameters. Since the nominal plant is not assumed to satisfy the Davison condition, the possibility of solving the problem actually depends on the knowledge of the dependence of the matrices describing the system on the unknown parameters