This thesis discusses the set-theoretic methods for constrained control of high-order systems. Specifically, focus of the thesis is given on the operating envelope protection and constrained time-optimal control design in the algebra of polyhedral sets, whereas the utility-scale wind turbine is used to validate the proposed methods. Generally, set-theoretic control design for high-order systems suffers from the computational intractability which is related to the complexity of the specific operations between the sets. Algorithms that are proposed in this dissertation alleviate respective shortcomings. The developed set-theoretic methods are completely executed offline, whereas the computational cost for the on-line operation of the resulting control law is reduced to a minimum. Thus, a hard real-time claims can be posed, which is an important property for the technical systems with high safety requirements. Among the others, scientific contributions of the thesis include: approximate set-theoretic methods for application to high-order systems, method for the set-theoretic operating envelope protection design for a nonlinear process, real-time algorithm to derive a solution to the set of two-dimensional linear inequalities, algorithm for the wind turbine overspeed and the structure overload protection, method for the clustering-based identification of piecewise affine multiple-input multiple-output models and procedure for the wind turbine time-optimal controller design based on the identified piecewise affine model of the wind turbine.