Finite frequency H∞ control of discrete linear parameter-varying systems

This paper addresses the H ∞ control problem for discrete-time linear parameter-varying (LPV) systems within a specific frequency range. Using the generalized Kalman–Yakubovich–Popov (GKYP) lemma, a novel linear matrix inequality (LMI) condition is proposed, which depends on time-varying parameters. Furthermore, considering the system’s asymptotic stability and the time-domain constraints, a new H ∞ gain-scheduled state feedback controller design method is introduced. This method achieves the desired control objectives with a reduced number of LMI conditions. The proposed control method is validated through a 6-degree-of-freedom (DOF) half-car model with time-varying sprung mass. Simulation results demonstrate that the proposed control strategy is effective within the 4–8 Hz vibration frequency range, which corresponds to human sensitivity, while also ensuring compliance with actuator saturation constraints and suspension displacement time-domain limits.