Finite-Time Observer-Based Sliding-Mode Control for Markovian Jump Systems With Switching Chain: Average Dwell-Time...

Area of Science:

• Control Theory
• Systems Engineering
• Stochastic Systems

Background:

• Stochastic Markovian jump systems (MJSs) are complex systems with inherent uncertainties.
• Time-varying delays and packet losses (PLs) significantly challenge system stability and control.
• Deterministic switching chains (DSC) add another layer of complexity to MJS analysis.

Purpose of the Study:

• To develop a finite-time observer-based sliding-mode control (SMC) strategy.
• To address the challenges posed by stochastic MJSs with DSC, time-varying delays, and PLs.
• To guarantee finite-time boundedness within a specified time interval for the addressed system.

Main Methods:

• Modeling stochastic MJSs with DSC and characterizing PLs using Bernoulli random variables.
• Designing a nonfragile, finite-time bounded sliding-mode observer.
• Employing stochastic analysis techniques and the average dwell time (ADT) method.
• Developing a robust finite-time sliding-mode controller for state estimation.

Main Results:

• Sufficient criteria for guaranteeing finite-time boundedness are derived.
• The designed observer ensures finite-time boundedness of the system states.
• The controller ensures the reachability of the common sliding surface in the estimation space.
• The effectiveness of the proposed approach is validated through a numerical example.

Conclusions:

• The proposed finite-time observer-based SMC approach effectively manages stochastic MJSs with DSC, time-varying delays, and PLs.
• The method guarantees finite-time boundedness and robust controller design.
• This research offers a valuable framework for controlling complex, uncertain dynamic systems.