A novel approach to delay-fractional-dependent stability criterion for linear systems with interval delay

Area of Science:

• Control Theory
• Systems Engineering
• Applied Mathematics

Background:

• Stability analysis is crucial for linear systems with time-varying delays.
• Existing methods often suffer from conservatism due to approximations.
• Accurate analysis requires incorporating delay interval information effectively.

Purpose of the Study:

• To develop a novel delay-fractional-dependent stability criterion for linear systems with interval time-varying state delay.
• To reduce conservatism in stability analysis by fully utilizing delay information.
• To improve the accuracy of stability analysis for systems with variable delays.

Main Methods:

• A delay variable decomposition approach is employed to segment the delay interval.
• Lyapunov-Krasovskii (LK) functional is utilized without direct approximation of its time-derivative.
• Jensen integral inequalities and convex combination techniques are applied.
• Variable Lyapunov matrices are chosen for different delay subintervals for reduced conservatism.

Main Results:

• A new stability criterion is derived that accounts for delay intervals.
• The proposed method demonstrates reduced conservatism compared to existing approaches.
• Numerical examples confirm the effectiveness and improved performance of the method.

Conclusions:

• The developed delay-fractional-dependent stability criterion offers a less conservative approach.
• The delay variable decomposition and improved LK functional estimation enhance analysis accuracy.
• The method is effective for stability analysis of linear systems with interval time-varying state delays.