Output feedback H_∞ control for singular hybrid systems with partly unknown transition rates and input saturation

Area of Science:

• Control Systems Engineering
• Systems Theory
• Stochastic Systems

Background:

• Singular Markovian jump systems present unique control challenges due to their complex dynamics and state-dependent parameters.
• Input saturation and partly unknown transition rates further complicate the design of robust controllers.

Purpose of the Study:

• To develop a dynamic output feedback H∞ control strategy for singular Markovian jump systems.
• To address challenges posed by input saturation and partly unknown transition rates.
• To ensure stochastic admissibility and H∞ performance for the closed-loop system.

Main Methods:

• Derivation of necessary and sufficient conditions for stochastic admissibility and H∞ performance using linear matrix inequalities (LMIs).
• Design of a mode-dependent dynamic output feedback controller.
• Proposal of a novel set invariant condition for estimating the attraction domain.
• Formulation of attraction domain estimation as an LMI optimization problem.

Main Results:

• Necessary and sufficient conditions for stochastic admissibility and H∞ performance were established.
• A mode-dependent dynamic output feedback controller was successfully designed.
• A novel set invariant condition was introduced, enabling attraction domain estimation.
• The method was validated through a numerical example and an oil catalytic cracking process.

Conclusions:

• The proposed dynamic output feedback H∞ control method effectively guarantees stochastic admissibility and H∞ performance for singular Markovian jump systems.
• The novel set invariant condition provides a robust way to estimate the system's attraction domain, enhancing performance analysis.
• The approach is practical and validated for real-world applications.