Control of Linear Systems with Guarantee of Outputs in Given Sets at Any Time

A new method for designing the control law for linear plants with a guarantee of finding outputs in given sets under conditions of unknown bounded disturbances is proposed. The problem is solved in two stages. In the first stage, a coordinate transformation is used to reduce the original constrained problem to the problem of studying the input-to-state stability of a new extended system without constraints. In the second stage, the control law for the transformed system is designed, where the adjustable parameters are selected from the solution of linear matrix inequalities (LMI). The simulations, which are performed in MATLAB, show the method's efficiency and confirm the theoretical results.