Robust Sampled-Data State-Derivative Feedback Control Design for LTI Systems With Polytopic Uncertainty

This letter addresses the design of robustly stabilizing control laws for linear time-invariant (LTI) systems with polytopic uncertainty using sampled-data state-derivative feedback. The proposed approach is based on a hybrid model description of the closed-loop system, with jumps occurring at the sampling instants. We present sufficient convex conditions in the form of linear matrix inequalities (LMIs) and differential linear matrix inequalities (DLMIs) for the synthesis of the controller. The proposed conditions include a scalar design parameter, which can be used to tune the transient response of the closed-loop system. An example involving a benchmark system borrowed from the literature is presented for illustration.