Robustness with respect to delay uncertainties of a predictor-observer based discrete-time controller

This paper focuses on the delay-dependent stability problem of a discrete-time prediction scheme to stabilize possible unstable continuous-time systems. The delay-dependent stability condition is expressed in terms of LMIs. The separation principle between the proposed predictor and a state observer is also proved. The closed-loop system is shown to be robust with respect to uncertainties in the knowledge on the plant parameters, the delay and the sampling period. The proposed scheme has been tested in a real-time application to control the roll angle in a prototype of a quad-rotor mini-helicopter

I. Introduction

The Smith Predictor (SP) [8] and finite spectrum assignment (FSA) [4] may be considered as the main control methods for linear processes that have a delay in their input or output [2]. A careful analysis of these methods and their modifications show that they all use, in an explicit or explicit manner, prediction of the state in order to achieve the control of the system. A common drawback, linked to the internal instability of the prediction, is that they fail to stabilize unstable systems.