Compensation of Input/Output Delays for Retarded Systems by Sequential Predictors: A Lyapunov-Halanay Method

TL;DR

This paper introduces a Lyapunov-Halanay method utilizing sequential predictors to achieve global asymptotic stabilization of nonlinear retarded systems with large input/output delays, extending to systems with less restrictive stabilizability conditions.

Contribution

It develops a novel predictor-based control approach for retarded systems with delays, including output delays, under broad stabilizability and observability conditions.

Findings

Effective stabilization of delayed systems demonstrated on a pendulum example.

Extension of predictor-based control to systems with ISS conditions.

Achieved GAS despite large input/output delays.

Abstract

This paper presents a Lyapunov-Halanay method to study global asymptotic stabilization (GAS) of nonlinear retarded systems subject to large constant delays in input/output - a challenging problem due to their inherent destabilizing effects. Under the conditions of global Lipschitz continuity (GLC) and global exponential stabilizability (GES) of the retarded system without input delay, a state feedback controller is designed based on sequential predictors to make the closed-loop retarded system GAS. Moreover, if the retarded system with no output delay permits a global exponential observer, a dynamic output compensator is also constructed based on sequential predictors, achieving GAS of the corresponding closed-loop retarded system with input/output delays. The predictor based state and output feedback stabilization results are then extended to a broader class of nonlinear retarded systems with input/output delays, which may not be GES but satisfy global asymptotic stabilizability/observability and suitable ISS conditions. As an application, a pendulum system with delays in the state, input and output is used to illustrate the effectiveness of the proposed state and output feedback control strategies based on sequential predictors.