A Geometric Algebra Approach to Invariance Control in Sliding Regimes for Switched Systems

Within a Geometric Algebra (GA) framework, this article presents a general method for synthesis of sliding mode (SM) controllers in Single Input Single Output (SISO) switched nonlinear systems. The method, addressed as the invariance control method, rests on a reinterpretation of the necessary and sufficient conditions for the local existence of a sliding regime on a given smooth manifold. This consideration leads to a natural decomposition of the SM control scheme resulting in an invariance state feedback controller feeding a Delta–Sigma modulator that, ultimately, provides the required binary-valued switched input to the plant. As application examples, the obtained results are used to illustrate the design of an invariance controller for a switched power converter system. Using the invariance control design procedure, it is shown how well-known second order sliding regime algorithms can be obtained, via a limiting process, from traditional sliding regimes induced on linear sliding manifolds for certain nonlinear switched systems.