Reachable set estimation for switched linear systems with state-dependent switching and bumpless transfer based...

Area of Science:

• Control Systems Engineering
• Systems Theory
• Applied Mathematics

Background:

• Switched linear systems present challenges in stability analysis and controller design due to their dynamic nature.
• Event-triggered control offers potential for reduced system burden compared to time-triggered approaches.
• Bumpless transfer is crucial for maintaining system performance during state transitions in switched systems.

Purpose of the Study:

• To develop an event-triggered control strategy for switched linear systems with state-dependent switching.
• To estimate the reachable set of the switched system under the proposed control mechanism.
• To design a state-feedback controller that guarantees system states remain within a predefined ellipsoid.

Main Methods:

• Utilizing the multiple Lyapunov functions method for reachable set estimation.
• Co-designing the event-triggered mechanism, switching law, and controller gain.
• Establishing a positive lower bound on inter-execution intervals to prevent Zeno behavior.

Main Results:

• The proposed event-triggered mechanism ensures bumpless transfer performance.
• Reachable set estimation is achieved for the switched system.
• A state-feedback controller is designed to confine system states within a preset ellipsoid.
• The absence of Zeno behavior is mathematically proven.

Conclusions:

• The developed event-triggered control strategy effectively addresses reachable set estimation and state-feedback controller design for switched linear systems.
• The co-design approach ensures stability, bumpless transfer, and avoids Zeno behavior.
• Numerical examples validate the theoretical framework and demonstrate practical applicability.