Further results on delay-dependent stability for continuous system with two additive time-varying delay components.

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Applied Mathematics

Background:

• Stability analysis is crucial for continuous systems with time delays.
• Time-varying delays introduce significant challenges in stability assessment.
• Existing methods often yield conservative results.

Purpose of the Study:

• To develop a less conservative stability criterion for continuous systems with two additive time-varying delays.
• To propose a novel Lyapunov-Krasovskii functional incorporating marginally delayed states.
• To provide a computationally efficient stability analysis method.

Main Methods:

• Construction of a novel Lyapunov-Krasovskii functional.
• Utilizing information from marginally delayed states.
• Application of reciprocal convex and convex polyhedron techniques for tighter upper bounds.
• Formulation of stability conditions as linear matrix inequalities (LMIs).

Main Results:

• A new delay-dependent stability criterion is derived.
• The proposed method offers less conservative results compared to existing approaches.
• The criterion is expressed in an LMI form, facilitating practical implementation.
• Numerical examples validate the effectiveness and reduced conservatism of the method.

Conclusions:

• The developed method effectively analyzes stability for systems with multiple time-varying delays.
• The use of advanced bounding techniques and a novel functional leads to improved stability results.
• The LMI formulation ensures ease of application and verification using standard tools.