Revina T. On positional synthesis for robust linear systems

A synthesis problem for one class of linear robust systems with continuous bounded unknown perturbations is studied, that is, the problem of constructing a control as a function of state coordinates satisfying predetermined constraints. Cases of one-dimensional as well as multi-dimensional control are considered. Constraints for unknown perturbations are found such that the control which solves the synthesis problem for a linear system without perturbations also solves the synthesis problem for a perturbed system. The time of motion from an arbitrary initial point to the origin is estimated both from below and from above. As an example of application of obtained results control problems for some mechanical systems with uncertain parameters are considered.