Quantized Feedback Control of Fuzzy Markov Jump Systems.

Area of Science:

• Control Systems Engineering
• Nonlinear Systems Theory
• Stochastic Systems Analysis

Background:

• Nonlinear Markov jump systems (MJSs) with time-varying delays present significant control challenges.
• Quantized feedback control is essential for practical implementation but introduces complexities.
• Takagi-Sugeno fuzzy models offer a framework for representing nonlinear MJSs.

Purpose of the Study:

• To develop a quantized feedback controller for nonlinear MJSs with time-varying delays.
• To ensure the stochastic stability and a predefined $l_2$-$l_\infty$ performance of the closed-loop system.
• To convert the controller design into a solvable convex optimization problem.

Main Methods:

• Utilizing a Takagi-Sugeno fuzzy model to represent the nonlinear MJS.
• Employing the sector bound approach to handle quantization errors.
• Constructing a mode-dependent Lyapunov function and applying the reciprocally convex approach.
• Leveraging linear matrix inequality (LMI) techniques for controller design.

Main Results:

• A criterion for guaranteeing stochastic stability and $l_2$-$l_\infty$ performance is derived.
• The quantized feedback controller design is formulated as a convex optimization problem.
• Simulation results demonstrate the effectiveness and practicality of the proposed method.

Conclusions:

• The proposed quantized feedback control strategy effectively addresses nonlinear MJSs with time-varying delays.
• The integration of fuzzy logic, Lyapunov stability theory, and LMI techniques provides a robust solution.
• The method offers a practical approach for implementing quantized control in complex systems.