Event-Triggered Reduced-Order Filtering for Continuous Semi-Markov Jump Systems With Imperfect Measurements

Area of Science:

• Control Systems Engineering
• Stochastic Systems Analysis
• Signal Processing

Background:

• Semi-Markov jump systems are complex due to their state-dependent transition probabilities.
• Imperfect measurements and randomly occurring uncertainties (ROUs) challenge filter design.
• Event-triggered filtering aims to reduce communication and computational load.

Purpose of the Study:

• To design an event-triggered reduced-order filter for continuous-time semi-Markov jump systems.
• To address challenges posed by polytopic, sojourn-time-dependent transition probability matrices (TPMs) and signal quantization.
• To account for randomly occurring uncertainties (ROUs) and sensor failures.

Main Methods:

• Utilizing a dissipativity-based technique to guarantee asymptotical stability and dissipative performance of the filtering error system.
• Employing a polytopic representation for the time-varying TPM and fractionalizing it for enhanced results.
• Introducing slack symmetric matrices and a cone complementarity linearization algorithm for filter parameter derivation.

Main Results:

• Sufficient conditions for the existence of the event-triggered reduced-order filter were established.
• The proposed filter ensures asymptotical stability with strict dissipative performance for the filtering error system.
• Simulation results validated the effectiveness of the developed event-triggered reduced-order filter design.

Conclusions:

• The developed event-triggered reduced-order filter effectively handles semi-Markov jump systems with complex uncertainties and imperfect measurements.
• The dissipativity-based approach provides a robust framework for ensuring system stability and performance.
• The method offers a practical solution for real-world applications requiring efficient filtering under challenging conditions.