IPR-based distributed interval observers design for uncertain LTI systems

Area of Science:

• Control Systems Engineering
• Systems Theory

Background:

• Distributed observers are crucial for monitoring complex systems.
• Estimating system states with uncertainties requires robust observer designs.
• Linear Time Invariant (LTI) systems are fundamental in control theory.

Purpose of the Study:

• To design a novel distributed interval observer for LTI systems with disturbances.
• To ensure the stability and positivity of the observer error system.
• To estimate the upper and lower bounds (ULBs) of system states using partial information.

Main Methods:

• Utilizing Internal Positive Representations (IPRs) for observer construction.
• Employing a synchronizing region approach for error system stability.
• Implementing distributed estimation with neighbor information exchange.

Main Results:

• The proposed observer effectively estimates the ULBs of LTI system states.
• The observer design guarantees a stable and positive error system.
• Numerical simulations validate the observer's performance.

Conclusions:

• The novel distributed interval observer is effective for LTI systems with disturbances.
• The IPRs and synchronizing region approach provide a robust design methodology.
• The method allows state estimation using limited output information and local interactions.