Event-Triggered Stabilizing Bit Rate Conditions for an n-Dimensional Linear System With i.i.d. Feedback Dropouts

Area of Science:

• Control Systems Engineering
• Networked Systems
• Digital Communications

Background:

• Linear time-invariant (LTI) systems are crucial in many engineering applications.
• Digital communication networks introduce challenges like delay and data packet dropouts.
• System stability can be compromised by network imperfections and internal state coupling.

Purpose of the Study:

• To develop a strategy for stabilizing LTI systems with feedback over unreliable digital networks.
• To reduce the required bit rate for feedback transmission while maintaining system stability.
• To address challenges posed by network delay, feedback dropouts, and state variable coupling.

Main Methods:

• Proposed a periodic event-triggering strategy for feedback control.
• State is measured periodically but transmitted only when a trigger condition is met.
• Utilized information from transmitted packets and sampling time instants to ensure stability.

Main Results:

• Achieved mean square stability at a lower bit rate compared to conventional periodic sampling.
• Derived stabilizing bit rate conditions dependent on delays, dropout rates, and system eigenvalues.
• Demonstrated that process noise and lack of direct state access do not negatively impact stabilizing bit rate.

Conclusions:

• The proposed periodic event-triggering strategy effectively stabilizes LTI systems over networks with delays and dropouts.
• The strategy offers significant bandwidth savings compared to traditional methods.
• The derived conditions provide a clear framework for designing stable networked control systems.