Stabilization and Consensus of Linear Systems with Multiple Input Delays by Truncated Pseudo-Predictor Feedback

TL;DR

This paper introduces a truncated pseudo-predictor feedback method for stabilizing linear systems with multiple input delays, providing finite-dimensional controllers that can handle large bounded delays and solve consensus problems in multi-agent systems.

Contribution

It generalizes pseudo-predictor feedback to multiple delays and develops a finite-dimensional truncated version for practical stabilization and consensus in delayed linear systems.

Findings

TPPF can stabilize systems with large bounded delays.

The approach effectively solves consensus in multi-agent systems with delays.

Numerical examples confirm the method's effectiveness.

Abstract

This paper provides an alternative approach referred to as pseudo-predictor feedback (PPF) for stabilization of linear systems with multiple input delays. Differently from the traditional predictor feedback which is from the model reduction appoint of view, the proposed PPF utilizes the idea of prediction by generalizing the corresponding results for linear systems with a single input delay to the case of multiple input delays. Since the PPF will generally lead to distributed controllers, a truncated pseudopredictor feedback (TPPF) approach is established instead which gives finite dimensional controllers. It is shown that the TPPF can compensate arbitrarily large yet bounded delays as long as the open-loop system is only polynomially unstable. The proposed TPPF approach is then used to solve the consensus problems for multi-agent systems characterized by linear systems with multiple input delays. Numerical examples show the effectiveness of the proposed approach.