Two-Dimensional Asynchronous Sliding-Mode Control of Markov Jump Roesser Systems

Area of Science:

• Control Theory
• Systems Engineering
• Stochastic Systems

Background:

• Investigating control strategies for 2-D discrete-time Markov jump systems.
• Addressing challenges of asynchronous system modes and controller accessibility.
• Utilizing hidden Markov models for mode uncertainty.

Purpose of the Study:

• To design an asynchronous sliding-mode control (SMC) law for 2-D discrete-time Markov jump systems.
• To ensure asymptotic mean-square stability (AMSS) and H∞ disturbance attenuation.
• To develop a method for deriving the asynchronous 2D-SMC law.

Main Methods:

• Construction of a novel 2-D sliding surface.
• Design of an asynchronous SMC law within a hidden Markov model framework.
• Application of Lyapunov functions and linear matrix inequality (LMI) techniques.

Main Results:

• Establishment of sufficient conditions for system reachability to the sliding surface.
• Guaranteed asymptotic mean-square stability (AMSS) for the 2-D system.
• Demonstrated H∞ disturbance attenuation performance.

Conclusions:

• The proposed asynchronous SMC law is effective for 2-D discrete-time Markov jump systems.
• The developed algorithm provides a valid approach for designing the control law.
• The method ensures system stability and performance under mode uncertainty.