New results on delay-range-dependent stability analysis for interval time-varying delay systems with non-linear...

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Systems Theory

Background:

• Interval time-varying delay systems are crucial in many applications but challenging to analyze due to time delays and nonlinearities.
• Existing stability criteria often exhibit conservatism, limiting their practical applicability.
• Lyapunov-Krasovskii functionals (LKF) are standard tools for stability analysis, but their effectiveness can be enhanced.

Purpose of the Study:

• To develop a novel, less conservative stability criterion for interval time-varying delay systems with nonlinear perturbations.
• To improve the accuracy and efficiency of stability analysis for such complex systems.
• To provide a delay-range-dependent stability condition.

Main Methods:

• Utilizing Lyapunov-Krasovskii functionals (LKF) for stability analysis.
• Employing linear matrix inequality (LMI) techniques.
• Applying integral inequality approach (IIA) and delayed decomposition approach (DDA).
• Segmenting the delay range into two equal parts for analysis.

Main Results:

• A sufficient delay-range-dependent criterion for asymptotic stability was derived.
• The proposed method demonstrated reduced conservatism compared to existing approaches.
• Theoretical and numerical comparisons confirmed the method's effectiveness and efficiency.
• Validation through two well-known examples.

Conclusions:

• The developed method provides an effective and less conservative approach for stability analysis of interval time-varying delay systems.
• The combination of LKF, LMI, IIA, and DDA offers significant improvements in stability analysis.
• The findings contribute to the robust design and control of systems with time delays and nonlinearities.