Asynchronous Stabilization for Two Classes of Stochastic Switching Systems with Applications on Servo Motors

Area of Science:

• Control Theory
• Stochastic Systems
• System Stability

Background:

• Stochastic switching systems present unique challenges in stabilization due to asynchronous dynamics.
• Dual switching systems combine deterministic and stochastic dynamics, while semi-Markov jump systems involve time-dependent transitions.

Purpose of the Study:

• To develop novel stability criteria and controller design methods for asynchronous dual switching and semi-Markov jump systems.
• To address the challenges posed by inaccurate mode detection, time-varying delays, and uncertain transition probabilities.

Main Methods:

• Proposing new stability criteria that allow for controlled increases in Lyapunov functions during asynchronous intervals.
• Developing numerically testable asynchronous controller design methods for dual switching systems.
• Designing novel asynchronous controller methods for semi-Markov jump systems with bounded sojourn times.

Main Results:

• New stability criteria effectively handle asynchronous phenomena in both system types.
• The proposed controller design methods are practical for scenarios with mode mismatch and time delays.
• The methods for semi-Markov jump systems accommodate more realistic bounded sojourn times.

Conclusions:

• The developed techniques provide effective solutions for asynchronous stabilization problems in complex stochastic switching systems.
• The findings offer practical and less conservative approaches for controller design in these systems.