Reduced order dynamic controller synthesis conditions for LPV periodic discrete-time systems subject to input saturation

•Synthesis of reduced order controllers and anti-windup gains for LPV periodic discrete systems under saturation and noises.•The procedure is separated into three stages, each composed by convex conditions, leading to the desired control system.•The conservativeness of the conditions can be reduced by knowing the variation rates bounds of the time-varying parameters.•Two algorithms are proposed, the first to maximize the system robustness and the second to maximize the region of attraction.•Analysis of the methodology using a numerical example, showing how modifications to the three stages may affect the result.