Control of MIMO linear plants with a guarantee for the controlled signals to stay in a given set

In this paper, we propose a new method for synthesizing the control of multi-input multi output linear plants with a guarantee of finding controlled signals in given sets under conditions of unknown bounded disturbances. The problem is solved in two stages. At the first stage, the coordinate transformation method 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. At the second stage, the control law for the extended system is obtained by solving a series of linear matrix inequalities. To illustrate the effectiveness of the proposed method, simulation in the MATLAB/Simulink is given. The simulation results show the presence of controlled signals in the given sets and the boundness of all signals in the control system. The proposed method is recommended for use in control problems where it is required to maintain controlled signals in given sets, for example, control of an electric power network, control of the reservoir pressure maintenance process, etc.