An improved sufficient condition for stabilisation of unstable first-order processes by observer-state feedback

Abstract

This work considers the stabilisation and control of unstable first-order linear systems subject to a relatively large I/O time delay. First, it is proposed an observer strategy to predict a specific internal signal in the process. The adequate prediction convergence is obtained and formally stated. Then, it is proposed an estimated state feedback control. Necessary and sufficient stability conditions with respect to time delay size and unstable time constant are provided. The proposed control strategy allows to address time delays as large as four times the unstable time constant of the open-loop system, in contrast with most of the reported related literature. Numerical examples are used for illustrating the parametric stabilisation region as a function of the time delay.

Keywords:

• unstable processes
• I/O delay
• observer-based feedback
• stabilisation

Additional information

Funding

J.F. Marquez-Rubio acknowledges postdoctoral financial support by CONACyT under grant number CVU 210823.