New optimal analysis method to stability and H_∞ performance of varying delayed systems

Area of Science:

• Control Systems Engineering
• Systems Theory
• Nonlinear Dynamics

Background:

• Interval time-varying delay systems present challenges in stability and performance analysis.
• Existing methods often suffer from conservatism, limiting their practical applicability.
• Optimizing analysis techniques is crucial for robust control system design.

Purpose of the Study:

• To develop a novel, less conservative analysis method for interval time-varying delay systems.
• To enhance the stability analysis and H-infinity performance assessment.
• To effectively integrate Lyapunov-Krasovskii functionals (LKF) with advanced estimation techniques.

Main Methods:

• Construction of a new augmented vector and a Lyapunov-Krasovskii functional (LKF) incorporating triple integral terms.
• Utilization of two distinct integral inequalities to couple the LKF with estimation techniques.
• Development of criteria to reduce conservatism in stability and H-infinity performance analysis.

Main Results:

• A novel, integrated approach for analyzing interval time-varying delay systems.
• Reduced conservatism in stability and H-infinity performance criteria compared to existing methods.
• Demonstrated superiority of the proposed methods through numerical examples.

Conclusions:

• The proposed method offers a more effective way to analyze stability and H-infinity performance.
• The integration of LKF and estimation techniques significantly reduces analysis conservatism.
• The findings provide a valuable tool for designing more robust control systems.