Set‐based gain‐scheduled control via quasi‐convex difference inclusions

Abstract

A nonlinear system with sector-bounded nonlinearities may be expressed as a quasi-linear parameter-varying (LPV) system (convex combination of linear models), being this a well-known fact. The convex difference inclusion (CDI) modeling framework proposed by Fiacchini and coworkers in several of their works generalizes the quasi-LPV modeling procedure and proposes robust controllers enlarging polytopic domain of attraction estimates. This works further generalizes the CDI approach to a gain-scheduled case including, also, some quasi-convex cases. Controller design is based on convexity properties of two set valued maps describing (with some uncertainty) the state evolution and the state-dependent set where scheduling variables take values. As most set-based approaches, the proposal is tractable in low-dimensional cases. The presented results encompass prior quasi-LPV and CDI models as particular cases.