A Two-Step Design for Robust Input-Output Decoupling of a Class of Uncertain and Linear Parameter Dependent Systems

This research delves into the intricacies of achieving input-output decoupling for a class of uncertain linear parameter dependent systems. A combined approach is introduced, involving the utilization of a state feedback controller that incorporates both static and time-varying elements. The design of this controller aims to maintain insensitivity to uncertainties. The investigation establishes criteria for determining the feasibility of solving the robust input-output decoupling problem. Under these established conditions, a specific class of state feedback controllers is systematically identified as proficient in effectively addressing the stated problem. The proposed methodology entails deriving the controller and formulating solvability conditions to convert the original Parameter Dependent System (PDS) into an uncertain Linear Time-Invariant (L TI) system. Then an analytical presentation of a static state feedback controller is provided as a mean to resolve the input-output robust decoupling for the uncertain L TI system. The practical applicability of these findings is exemplified through successful implementation in a two-mass translation system, appropriately linked with a hydraulic actuator.