Reciprocal convex approach to output‐feedback control of uncertain LPV systems with fast‐varying input delay

Robust control of parameter‐dependent input delay linear parameter‐varying (LPV) systems via gain‐scheduled dynamic output‐feedback control is considered in this paper. The controller is designed to provide disturbance rejection in the context of the induced ‐norm or the norm of the closed‐loop system in the presence of uncertainty and disturbances. A reciprocally convex approach is employed to bound the Lyapunov‐Krasovskii functional derivative and extract sufficient conditions for the controller characterization in terms of linear matrix inequalities (LMIs). The approach does not require the rate of the delay to be bounded, hence encompasses a broader family of input‐delay LPV systems with fast‐varying delays. The method is then applied to the air‐fuel ratio (AFR) control in spark ignition (SI) engines where the delay and the plant parameters are functions of the engine speed and mass air flow. The objectives are to track the commanded AFR signal and to optimize the performance of the three‐way catalytic converter (TWC) through the precise AFR control and oxygen level regulation, resulting in improved fuel efficiency and reduced emissions. The designed AFR controller seeks to provide canister purge disturbance rejection over the full operating envelope of the SI engine in the presence of uncertainties. Closed‐loop simulation results are presented to validate the controller performance and robustness while meeting AFR tracking and disturbance rejection requirements.