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Finite-Time Stability Analysis and Stabilization of Switched Affine Systems via an Event-Triggered Strategy
IEEE Transactions on Cybernetics
|July 8, 2024
Summary
This study introduces a novel two-step hybrid control scheme for switched affine systems, addressing finite-time control challenges with an event-triggered mechanism (ETM). The method ensures practical stability and finite-time stabilization while avoiding Zeno behavior.
Area of Science:
- Control Theory
- Systems Engineering
- Applied Mathematics
Background:
- Finite-time control of switched affine systems presents significant analytical challenges due to affine terms.
- Designing globally feasible event-triggered mechanisms (ETMs) within a finite-time control framework is complex.
- Existing methods struggle to effectively manage the interplay between affine dynamics and event-triggered control.
Purpose of the Study:
- To develop a robust finite-time control strategy for switched affine systems using an event-triggered approach.
- To design a two-step hybrid control scheme that ensures both practical stability and finite-time stabilization.
- To exclude Zeno behavior in the event-triggered mechanism while guaranteeing system performance.
Main Methods:
- A two-step hybrid control scheme is proposed, separating practical stability and finite-time stabilization.
- An event-triggered mechanism (ETM) is designed by intersecting affine term thresholds with feasible state regions to prevent Zeno behavior.
- An affine state-dependent switching law and sufficient conditions are derived for practical stability, with settling time estimation.
- Criteria for finite-time stabilization are presented, along with an overall settling-time upper bound derivation.
Main Results:
- The proposed method successfully achieves practical stability for switched affine systems under an event-triggered strategy.
- Zeno behavior is effectively excluded through the intersection of affine term thresholds and feasible state regions within the ETM.
- Finite-time stabilization is achieved, with derived criteria and an upper bound for the overall settling time.
- A numerical example validates the effectiveness of the developed control scheme.
Conclusions:
- The novel two-step hybrid control scheme provides an effective solution for the finite-time control of switched affine systems via ETM.
- The method guarantees practical stability and finite-time stabilization while ensuring the absence of Zeno behavior.
- The derived conditions and settling-time estimations offer valuable insights for practical implementation.
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