Stability of nonlinear stochastic systems under event-triggered impulsive control with distributed-delay impulses

Area of Science:

• Control Theory
• Nonlinear Systems
• Stochastic Systems

Background:

• Impulsive control systems are crucial for managing complex dynamics.
• Distributed delays and stochasticity introduce significant stability challenges.
• Event-triggered impulsive control (ETIC) offers efficient data transmission.

Purpose of the Study:

• To investigate the stability of nonlinear stochastic systems with distributed-delay impulses under ETIC.
• To propose novel continuous and periodic event-triggered mechanisms (ETMs) that avoid Zeno behavior.
• To establish sufficient conditions for p-th moment uniform stability (p-US) and p-th moment exponential stability (p-ES).

Main Methods:

• Lyapunov method and mathematical induction for stability analysis.
• Development of continuous and periodic event-triggered mechanisms (ETMs).
• Linear Matrix Inequality (LMI) approach for joint design of ETM and control gains.

Main Results:

• Sufficient conditions derived for ensuring p-US and p-ES in systems with distributed-delay impulses.
• Proposed ETMs effectively eliminate Zeno behavior.
• Successful application to nonlinear stochastic systems, demonstrating feasibility through numerical examples.

Conclusions:

• The proposed ETIC framework provides a robust method for stabilizing nonlinear stochastic systems with distributed delays.
• The joint design using LMI ensures effective control and stability.
• Numerical simulations confirm the practical applicability and effectiveness of the theoretical findings.