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 the linear combination of the uncertain time-varying parameters including time-invariant parametric uncertainties (TIPU). It is supposed that these uncertainties are bounded by the given intervals and cannot be pulled out as an uncertain block. It is considered a serious challenge because the exact information about the plant dynamics cannot be extracted from the uncertain time-varying parameters. This is while; the gain-scheduled controllers need to have the exact information about the plant dynamics to satisfy the desired control purposes. To handle this challenge, we introduce a state-feedback gain, which is formed by a set of the new scheduling parameters and a secondary time-varying term. The stabilization conditions are obtained in terms of the linear matrix inequalities (LMIs). The effectiveness of the proposed method is shown using an example.