In this paper, we propose original methods for the synthesis of invariant systems considering the constraints on the components of the state vector and control. A two-step procedure for the synthesis of the problem of ensuring invariance with a given accuracy is developed by expanding the space of states. We used discontinuous functions at the input of integrators, which generate sliding motions in each of the subsystems over a finite time span to solve the stabilization problem. The synchronous generator is considered as an example of application; the numerical simulation results obtained in Matlab showed the high efficiency of the proposed approach.