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.

在几何代数 (GA) 框架内，本文介绍了在单输入单输出 (SISO) 切换非线性系统中合成滑模 (SM) 控制器的一般方法。该方法，称为不变性控制方法，基于对给定光滑流形上滑动状态局部存在的必要和充分条件的重新解释。这种考虑导致 SM 控制方案的自然分解，从而产生一个不变状态反馈控制器，为 Delta-Sigma 调制器供电，最终为设备提供所需的二进制值开关输入。作为应用实例，所获得的结果用于说明开关功率变换器系统的不变性控制器的设计。使用不变性控制设计程序，展示了如何通过限制过程从某些非线性切换系统的线性滑动流形上诱导的传统滑动状态获得众所周知的二阶滑动状态算法。