New Results on Memory Sampled-Data Control Design for IT2 Fuzzy Singular Systems With External Disturbance

Area of Science:

• Control Systems Engineering
• Fuzzy Logic Systems
• Nonlinear Systems Analysis

Background:

• Interval type-2 fuzzy singular systems (SSs) present unique control challenges due to their complexity and inherent uncertainties.
• External disturbances can significantly degrade the performance and stability of these systems.
• Existing sampled-data (SD) control methods often exhibit conservatism, limiting their applicability.

Purpose of the Study:

• To design a robust memory sampled-data (SD) controller for interval type-2 fuzzy singular systems (SSs).
• To reduce the conservatism associated with integral terms in stability analysis.
• To ensure system admissibility and achieve a specified H∞ disturbance attenuation level.

Main Methods:

• Development of an improved free-weighting matrix inequality to minimize conservatism.
• Construction of a novel looped-functional-based Lyapunov-Krasovskii functional (LKF) incorporating sampling interval data.
• Formulation of new admissibility conditions using linear matrix inequalities (LMIs).

Main Results:

• The proposed memory SD controller design guarantees system admissibility for interval type-2 fuzzy SSs.
• The new approach effectively reduces conservatism in stability analysis.
• Achieved H∞ disturbance attenuation demonstrates the controller's robustness against external disturbances.

Conclusions:

• The developed LMIs-based criteria provide a less conservative and effective method for designing memory SD controllers for fuzzy SSs.
• Numerical simulations validate the proposed method's usefulness and benefits in practical applications.
• This work advances the control theory for complex uncertain dynamical systems.