Pseudo predictor feedback stabilisation of linear systems with both state and input delays

Abstract

This paper is concerned with the stabilization of linear systems with both input and state delay by utilizing the predictor based delay compensation method. A pseudo predictor feedback control scheme is proposed, where the targeted closed-loop system is used for the prediction. This avoids the explicit dependence of the control input on past input data, and related instability problems in the implementation of the control law. It is proved that the stability of the closed-loop system is determined by the stability of the target closed-loop system, along with the stability of an associated integral delay system, which describes the additional dynamics induced by the pseudo predictor. In the considered case where the input delay is larger than the state delay the control law explicitly depends on the fundamental matrix of the system. It is shown that in case of commensurate delays, the control law can be directly expressed as a function of the original system matrices, while the stability of the integral delay system can be connected with the stability of an associated system with discrete delay, widening the applicability of analysis and design tools. For the synthesis of the feedback gains, a numerical procedure is presented to solve the simultaneous stabilization problem of the target system and the associated integral delay system. Numerical experiments are carried out to illustrate the effectiveness of the methodology.

Predictor-based control of time-delay systems: a survey

“…where φ(t) and Φ A (•, •) are defined in Table 1. Thereafter, the general principles of truncated predictorbased control were applied to design a novel integration-free method named "pseudo predictor-based controller" (Zhou, 2014a;Zhang, Zhou, & Michiels, 2021), in which the closed-loop dynamic was utilised to replace the open-loop system equation for designing the control law.…”