Design of Stable Feedback Controllers for Second Order Systems with Varying Sampling Rate: LQ and Lie-Algebraic Approaches

Abstract: In this article, we consider the design of a controller family that given a second-order continuous-time linear plant controlled at a varying rate, asymptotically stabilizes the closed loop and provides a good performance. Rate adaptation of control task execution is increasingly used in order to optimize allocation and throughput of shared resources in embedded systems. The LQ technique, tipically used to adapt the controller parameters to rate variation, is compared with a Lie-algebraic method [7] which guarantees the existence of a common Lyapunov function for the varying-time system. The use of a performance index as a function of the rate, derived from the discrete Lyapunov function and related with closed-loop eigenvalues, simplifies the evaluation of the cost associated with each rate