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Synthesis of Invariant Systems of a Given Accuracy Based on the Sliding Modes Theory

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.