Event-triggered impulsive control for input-to-state stability of nonlinear time-delay system with delayed impulse

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Systems Theory

Background:

• Input-to-state stability (ISS) is crucial for robust control systems.
• Nonlinear time-delay systems with impulses present significant control challenges.
• Existing control methods often struggle with flexible delays and external disturbances.

Purpose of the Study:

• To investigate input-to-state stability (ISS) for nonlinear time-delay systems with delayed impulses.
• To develop an event-triggered impulsive control (ETIC) strategy that avoids Zeno behavior.
• To propose sufficient conditions for achieving ISS in these complex systems.

Main Methods:

• Development of an event-triggered mechanism (ETM) using system state and disturbance information.
• Introduction of a forced impulse sequence to enhance feasibility and avoid Zeno behavior.
• Application of Lyapunov-Razumikhin-like methods to derive ISS conditions.
• Utilization of linear matrix inequalities (LMIs) for designing ETM and control gain.

Main Results:

• Sufficient conditions for achieving ISS in nonlinear time-delay systems with delayed impulses were formulated.
• A novel ETIC approach was proposed, effectively managing flexible delays and distinct external inputs.
• The proposed ETM and control design were validated through two numerical examples.

Conclusions:

• The study successfully established conditions for ISS in nonlinear time-delay systems under ETIC.
• The developed methods provide a robust framework for controlling systems with delayed impulses and disturbances.
• The findings contribute to the advancement of stability analysis and control design for complex dynamical systems.