On robust state derivative feedback control for uncertain polytopic systems with uncertain sampling period and network‐induced delay

Abstract

This paper addresses the state derivative feedback control problem for uncertain polytopic systems subject to an uncertain sampling period and network‐induced delay. The distinctive contribution relies on the direct design of a robust state derivative feedback controller employing an augmented discretized model derived in terms of the state derivative feedback such that network‐induced delay and uncertain sampling periods can be incorporated from the original continuous‐time state‐space representation into the discretized model. Two augmented models are provided to handle longer input time delays, as well as delays less or equal to the sampling period. In this work, all the uncertain parameters are modeled as a polytopic form whose resulting discrete‐time model has matrices with polynomial dependence on the uncertain parameters and an additive norm‐bounded term featuring the discretization residual error. Moreover, synthesis conditions are derived using a set of linear matrix inequalities (LMI) to solve the stabilization problem for this class of systems under different input time delays. Finally, numerical simulations are carried out to evaluate the effectiveness of the proposed method.