Linear variable parameter systems (LPV) are a very special class of nonlinear systems, which are suitable for controlling dynamic systems with parameter changes. Therefore, in this thesis, the problem of using variable parameter linear systems for controller design and stability analysis is raised. A designed controller must be able to reduce the adverse effects of disturbances in the output, for this purpose, in this research, by creating a compromise between the two functions of \(H_{2}\) and \(H_{\infty }\) and combining them with the anticipatory control of the resistant model, a suitable method can be used to eliminate the effect A disturbance was achieved. The controller designed in this research, while stabilizing the system, in the presence of external disturbance, reduces the effect of external disturbance on the output under the control of the system. In general, the purpose of presenting this research is to provide an effective algorithm for controlling a variable parameter linear system with disturbance using the robust model predictive control method, which method presented in this thesis is based on solving the linear matrix inequality, also the proposed method has the ability to consider It has different restrictions on system states and system output. All the results obtained in different sections, including stability analysis, controller performance analysis, are shown using several validated practical examples and their effectiveness. In this thesis, solving optimization problems in the environment is done, as well as the case solvers. It is used to obtain auxiliary and controlling matrices.
