Robust state-feedback controller for linear parameter-varying systems with time-invariant uncertainties

In this paper, the robust gain-scheduled state-feedback controller problem is studied for uncertain linear parameter-varying systems whose state-space representations are a linear combination of the uncertain time-varying parameters including time-invariant parametric uncertainties. It is supposed that these uncertainties are bounded by the given intervals and cannot be pulled out as an uncertain block. This is a serious challenge because the exact information about the plant dynamics cannot be extracted from the uncertain time-varying parameters, while the gain-scheduled controllers need to have the exact information about the plant dynamics in order to satisfy the desired control purposes. To handle this challenge, we introduce a state-feedback gain, which is formed by a set of new scheduling parameters and a secondary time-varying term. The stabilization conditions are obtained in terms of the linear matrix inequalities. The effectiveness of the proposed method is shown using an example. (c) 2023 Sharif University of Technology. All rights reserved.