Stability of uncertain impulsive complex-variable chaotic systems with time-varying delays

Area of Science:

• Control Theory
• Nonlinear Dynamics
• Chaos Theory

Background:

• Complex-variable chaotic systems exhibit sensitive dependence on initial conditions.
• Impulsive and delayed systems present unique control challenges due to discontinuous state changes and time lags.
• Parametric uncertainties and time-varying delays further complicate the stabilization of chaotic systems.

Purpose of the Study:

• To develop robust exponential stabilization criteria for uncertain impulsive complex-variable chaotic delayed systems.
• To account for parameter perturbations and delayed impulses in the system dynamics.
• To establish less conservative and easily verifiable stability conditions.

Main Methods:

• Adaptive control theory is employed to handle system uncertainties.
• Impulsive control techniques are utilized to manage discontinuous state transitions.
• Stability criteria are derived considering time-varying delays and parameter perturbations.

Main Results:

• Novel stability criteria for robust exponential stabilization are established.
• The proposed criteria are less conservative and easier to verify compared to existing methods.
• Effectiveness of the criteria is demonstrated through numerical simulations.

Conclusions:

• The developed criteria provide a reliable approach for stabilizing uncertain impulsive complex-variable chaotic delayed systems.
• The findings contribute to the theoretical understanding and practical control of complex chaotic dynamics.
• The proposed impulsive stabilization method is effective in the presence of uncertainties and delays.