Sliding mode control of switched systems: A geometric algebra approach

Geometric algebra (GA) is proposed as a mathematical framework for revisiting fundamental aspects of sliding mode control (SMC) in nonlinear, switch‐controlled, single input systems. Sliding mode existence conditions, the switching policy, the invariance conditions, the associated equivalent control, and the characterization of ideal sliding dynamics, are all re‐examined using a geometric algebra (GA) standpoint. Two illustrative examples, from switched power electronics, are presented using the GA language.