Compensation of Input/Output Delays for Retarded Systems by Sequential Predictors: A Lyapunov-Halanay Method
This addresses stabilization challenges in control systems with delays, such as in pendulum systems, but is incremental as it extends existing predictor methods to broader nonlinear retarded systems.
The paper tackles the problem of stabilizing nonlinear retarded systems with large constant input/output delays by designing state and output feedback controllers using sequential predictors, achieving global asymptotic stabilization under conditions like global Lipschitz continuity and exponential stabilizability.
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.