Output-Feedback stabilization for stochastic nonlinear systems with Markovian switching and time-varying powers

Area of Science:

• Control Theory
• Stochastic Systems
• Nonlinear Dynamics

Background:

• Stochastic nonlinear systems present significant control challenges.
• Markovian switching and time-varying powers add complexity to system stabilization.
• Existing methods often struggle with nonlinear growth rates.

Purpose of the Study:

• To develop an output-feedback stabilization strategy for stochastic nonlinear systems.
• To address systems with Markovian switching and time-varying powers.
• To extend stabilization techniques to systems with nonlinear growth rates.

Main Methods:

• Design of a reduced-order observer with a dynamic gain.
• Development of an output-feedback controller.
• Application of Itô's formula for Markovian switching systems.
• Advanced stochastic analysis techniques.

Main Results:

• The closed-loop system achieves an almost surely unique solution.
• System states are regulated to the origin with probability one.
• The proposed method handles nonlinear growth rates, a significant advancement.
• Demonstrated effectiveness through a simulation example.

Conclusions:

• The novel dynamic gain approach successfully stabilizes complex stochastic nonlinear systems.
• The method offers improved capabilities for systems with nonlinear dynamics and switching.
• This work advances the field of output-feedback control for stochastic systems.