New Stability Criterion for Positive Impulsive Fuzzy Systems by Applying Polynomial Impulse-Time-Dependent Method.

Area of Science:

• Control Systems Engineering
• Fuzzy Logic Systems
• Nonlinear Dynamical Systems

Background:

• Impulsive Takagi-Sugeno (T-S) fuzzy systems are widely used in control applications.
• Existing Lyapunov-based methods for stability analysis often yield conservative results due to limitations in handling time-varying impulse intervals.
• There is a need for less conservative approaches to analyze exponential stability and L1-gain for these systems.

Purpose of the Study:

• To develop a novel method for analyzing exponential stability and L1-gain of positive impulsive T-S fuzzy systems.
• To introduce a new class of Lyapunov functions that are dependent on impulse intervals.
• To derive less conservative conditions for stability analysis.

Main Methods:

• Construction of a novel polynomial impulse-dependent (ID) copositive Lyapunov function (CLF) using a polynomial impulse time function.
• Application of binomial coefficients to derive new finite linear programming conditions.
• Utilizing the enhanced information from the polynomial ID CLF for improved analysis.

Main Results:

• The proposed polynomial ID CLF captures more impulse interval information, leading to less conservative results.
• New finite linear programming conditions for stability and L1-gain analysis were derived.
• Demonstrated the influence of polynomial degree on the analysis results through three examples.

Conclusions:

• The developed polynomial ID CLF approach provides a less conservative and more effective method for analyzing positive impulsive T-S fuzzy systems.
• The new finite linear programming conditions offer practical tools for control system design.
• The study highlights the significance of impulse interval information in stability analysis.