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Sufficient condition for stabilization of linear time invariant fractional order switched systems and variable
Saeed Balochian1, Ali Khaki Sedigh
1Department of Electrical Engineering, Science And Research Branch, Islamic Azad University, Tehran, Iran. saeed.balochian@gmail.com
ISA Transactions
|September 20, 2011
Summary
This study stabilizes linear time-invariant fractional-order (LTI-FO) switched systems using a novel Lyapunov function approach. The variable structure control with a sliding sector ensures system stability for fractional orders between 1 and 2.
Area of Science:
- Control Theory
- Fractional Calculus
- System Stability
Background:
- Fractional-order systems present unique challenges in stability analysis.
- Switched systems require robust control strategies for reliable operation.
- Existing methods may not adequately address the complexities of LTI-FO switched systems.
Purpose of the Study:
- To develop a stabilization method for linear time-invariant fractional-order (LTI-FO) switched systems.
- To ensure stability for systems with fractional orders q where 1
- To design a control law based on Lyapunov stability theory and variable structure control.
Main Methods:
- Convex analysis and linear matrix inequality (LMI) for stability conditions.
- Extremum seeking method to construct a Lyapunov function.
- Variable structure control with a sliding sector for switching law design.
- Design of a switching control law to ensure Lyapunov function decrease.
Main Results:
- A sufficient condition for the stability of LTI-FO switched systems (1
- A single Lyapunov function with a negative derivative is successfully constructed.
- A sliding sector approach guarantees state-space coverage and Lyapunov function decrease.
- Simulation results validate the effectiveness of the proposed variable structure controller.
Conclusions:
- The proposed method effectively stabilizes LTI-FO switched systems.
- The combination of Lyapunov functions, extremum seeking, and variable structure control offers a robust solution.
- The developed controller ensures system stability within the specified fractional-order range.
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