Less Conservative Control Design for Linear Systems with Polytopic Uncertainties via State‐Derivative Feedback

Abstract

The motivation for the use of state‐derivative feedback instead of conventional state feedback is due to its easy implementation in some mechanical applications, for example, in vibration control of mechanical systems, where accelerometers have been used to measure the system state. Using linear matrix inequalities (LMIs) and a parameter‐dependent Lyapunov functions (PDLF) allowed by Finsler’s lemma, a less conservative approach to the controller design via state‐derivative feedback, is proposed in this work, with and without decay rate restriction, for continuous‐time linear systems subject to polytopic uncertainties. Finally, numerical examples illustrate the efficiency of the proposed method.