Bumpless transfer control for switched impulsive positive systems with L₁-gain performance

Area of Science:

• Control Theory
• Systems Engineering
• Applied Mathematics

Background:

• Switched impulsive positive systems present challenges due to control signal bumps arising from switching and impulsive effects.
• Existing control strategies may not adequately address bumpless transfer in these complex systems.

Purpose of the Study:

• To develop a bumpless transfer control strategy for switched impulsive positive systems.
• To achieve L1-gain performance while ensuring system positivity and minimizing control signal discontinuities.

Main Methods:

• Introduced a concept of bumpless transfer performance with magnitude constraints on control signals.
• Utilized a new class of multiple piecewise-continuous copositive Lyapunov functions.
• Designed a mode-dependent average dwell time switching signal bound and a bumpless transfer controller.

Main Results:

• Successfully designed a controller that ensures positive system properties.
• Achieved bumpless transfer by imposing constraints on control signal magnitudes.
• Guaranteed L1-gain performance for the closed-loop switched impulsive positive systems.

Conclusions:

• The proposed control strategy effectively addresses bumpless transfer in switched impulsive positive systems.
• The developed method demonstrates feasibility and superiority through simulations.
• This work provides a robust approach for enhancing control performance in systems with switching and impulsive dynamics.