Control of dynamical plants with a guarantee for the controlled signal to stay in a given set

We propose a control method for dynamical systems that permits one to guarantee that the plant output signal is in a given set at any time. To solve the problem, a special change of coordinates is used that permits one to reduce the original problem with constraints to the problem of studying the input-state stability of the new extended unconstrained system. Examples of coordinate changes are given, and control algorithms for linear plants and systems with a sector nonlinearity in the presence of parametric uncertainty and disturbances are synthesized. The results obtained are accompanied by modeling that illustrates the efficiency of our method and confirms the theoretical conclusions.