Observer-based event-triggered control of linear system with two-time scales.

Area of Science:

• Control Theory
• Systems Engineering
• Applied Mathematics

Background:

• Singularly perturbed systems are common in various engineering fields.
• Observer-based control is crucial for estimating system states.
• Event-triggered control aims to reduce communication and computation load.

Purpose of the Study:

• To develop an observer-based event-triggered control strategy for singularly perturbed systems.
• To ensure ultimately bounded stability of the closed-loop system.
• To eliminate Zeno behavior in the control system.

Main Methods:

• Designing two distinct event-triggering conditions for slow and fast subsystems.
• Utilizing state errors between observer and system models.
• Implementing a two-stage design for each event-triggering condition, incorporating observer error dynamics and absolute-type conditions.

Main Results:

• Achieved ultimately bounded stability for the closed-loop singularly perturbed system.
• Successfully eliminated Zeno behavior through the designed event-triggering conditions.
• Demonstrated the efficiency and feasibility of the proposed control strategy via numerical examples.

Conclusions:

• The proposed observer-based event-triggered control is effective for stabilizing singularly perturbed systems.
• The designed event-triggering conditions ensure system stability and avoid Zeno behavior.
• The method offers a practical approach for control design in relevant engineering applications.