Almost Sure Stabilization of Continuous-Time Jump Linear Systems via a Stochastic Scheduled Controller

Area of Science:

• Control Theory
• Stochastic Systems
• System Stability

Background:

• Continuous-time jump systems are complex due to abrupt changes.
• Ensuring stability (almost surely exponential stabilization) is crucial for reliability.
• Existing methods may struggle with systems lacking controllers in certain time slices.

Purpose of the Study:

• To develop a stochastic scheduled controller for almost surely exponential stabilization of continuous-time jump systems.
• To address scenarios where controllers are absent during specific time intervals.
• To provide solvable conditions for controller existence and analyze performance factors.

Main Methods:

• A stochastic scheduled controller based on the anytime algorithm is proposed.
• Novel techniques are applied to the stochastic transfer matrix.
• Sufficient conditions for controller existence are derived in solvable forms.

Main Results:

• The proposed controller effectively achieves almost surely exponential stabilization.
• Dwell times of the jump signal and stochastic scheduling properties positively impact performance.
• Solvable conditions for controller existence are established.

Conclusions:

• The developed stochastic scheduled controller is effective for continuous-time jump systems.
• The method offers improved performance and broader applications by considering dwell times and scheduling.
• The approach is validated through a practical example, demonstrating its superiority.