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The three way catalytic converter (TWC) is a critical component for the mitigation of tailpipe emissions of modern spark ignition internal combustion (IC) engines. Because the TWC operates effectively only when the air-fuel ratio is very close to stoichiometric, accurate control of the air-fuel ratio is required. This paper uses a switching linear parameter varying (LPV) controller to regulate the air-fuel ratio. For controller design purposes, the dynamics of the fuel path is modeled as a time-varying first-order plus dead time (FOPDT) model, varying with the engine operating point, i.e., engine speed and air flow. Large variation of the FOPDT model across the engine operating range leads to a conservative LPV controller. Therefore, the operating range is divided into smaller subregions, an individual LPV controller is designed for each, and the LPV controllers are then switched based on the operating point. The LPV controllers are found by solving a convex optimization problem with linear matrix inequalities (LMIs) which can be efficiently solved using available LMI techniques. The resulting closed-loop system has guaranteed performance over the operating range of the engine. Simulations show the improved air-fuel ratio regulation of the switching LPV controller over the engine's operating range compared to that of an H∞ controller which is scheduled based on air flow only as well as a non-switching LPV controller.