Output-feedback sampled-data control design for linear parameter-varying systems with delay

Abstract

In this paper, we address the sampled-data output-feedback control design problem for continuous-time linear parameter-varying systems with time-varying delay in the system states. Due to the combination of the plant's continuous-time dynamics and the controller's discrete-time dynamics connected through A/D and D/A converter devices, the closed-loop system is a hybrid system. In order to analyse this hybrid system from stability and performance perspectives we use the input-delay approach to map the closed-loop system into the continuous-time domain with delay in the states. This results in a closed-loop system containing two types of delays, the system internal delay and the one imposed by the mapping. Next, we use delay-dependent conditions for analysis of stability and -norm performance which result in a sampled-data control synthesis procedure. The proposed output-feedback sampled-data controller is obtained based on the solution to a linear matrix inequality optimisation problem using a set of appropriately defined slack variables. A numerical example of a milling machine is presented to demonstrate the viability of the proposed sampled-data control design method to satisfy the stability and performance objectives even with a varying sampling rate.