Further results on delay-range-dependent stability with additive time-varying delay systems.

Area of Science:

• Control Systems Engineering
• Systems Theory
• Applied Mathematics

Background:

• Time-varying delay systems are prevalent in network-based control systems.
• Stability analysis of these systems is crucial for reliable operation.
• Existing methods can be conservative, limiting the analysis of delays.

Purpose of the Study:

• To develop new delay-range-dependent stability conditions for time-varying delay systems.
• To propose a less conservative stability analysis framework.
• To enhance the analysis of systems with multiple time-varying delays.

Main Methods:

• Utilizing a Lyapunov-Krasovskii framework.
• Employing an integral inequality approach (IIA) for Leibniz-Newton formula terms.
• Constructing a novel Lyapunov-Krasovskii functional incorporating delay range information.
• Formulating criteria using linear matrix inequality (LMI).

Main Results:

• A new, less conservative delay-range-dependent stability criterion is established.
• The proposed method is effective for systems with two additive time-variant delays.
• Numerical examples demonstrate reduced conservatism and improved maximal allowable delay.

Conclusions:

• The developed criteria offer a simpler and less conservative approach to stability analysis.
• The methods are applicable to a general class of delay systems, particularly in network-based control.
• The findings contribute to more robust and reliable control system design.