Gain-scheduled inverse system and filtering system without derivatives of scheduling parameters

This paper considers a gain-scheduled inverse system for an LPV (linear parameter-varying) system based on the induced L₂ norm and proposes a method for its design. Usually, a gain-scheduled dynamic controller designed with a parameter-dependent Lyapunov function either requires derivatives of the scheduling parameters, or its existence condition is formulated with BMIs (bilinear matrix inequalities). However, in this paper we consider a gain-scheduled inverse system without derivatives of the scheduling parameters, and formulate the existence condition of a full-order gain-scheduled inverse system only with LMIs (linear matrix inequalities) despite using a parameter-dependent Lyapunov function. A gain-scheduled filtering system without derivatives of the scheduling parameters for an LPV system is also derived similarly. To demonstrate the effectiveness of the gain-scheduled right inverse system as a model-matching controller, a simple numerical example is presented and compared with an LTI (linear time-invariant) right inverse system.