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Probabilistic robust stabilization of fractional order systems with interval uncertainty
Baris Baykant Alagoz1, Celaleddin Yeroglu2, Bilal Senol2
1Department of Electrical and Electronics Engineering, Inonu University, Turkey.
ISA Transactions
|February 11, 2015
Summary
Fractional order perturbation significantly impacts robust stability in uncertain linear systems. This study introduces a probabilistic method to identify optimal fractional orders for enhanced system stability and robust control.
Area of Science:
- Control Theory
- Systems Engineering
- Applied Mathematics
Background:
- Linear time-invariant systems with interval uncertainty pose challenges for robust stability analysis.
- Fractional order calculus offers new possibilities for system analysis and control.
Purpose of the Study:
- To investigate the effects of fractional order perturbation on the robust stability of uncertain linear systems.
- To develop a probabilistic method for analyzing robust stability concerning fractional order.
- To establish a robust stabilization algorithm utilizing fractional order perturbation.
Main Methods:
- Developed a probabilistic stability analysis method using characteristic root region accommodation on the first Riemann sheet.
- Calculated stability probability distribution as a function of fractional order.
- Analyzed the dependence of robust stability on fractional order perturbation via order sensitivity of characteristic polynomials.
Main Results:
- Identified specific fractional order intervals that ensure robust stability for interval uncertain systems.
- Quantified the impact of fractional order perturbation on system robust stability.
- Demonstrated the effectiveness of the probabilistic approach in developing a robust stabilization algorithm.
Conclusions:
- Fractional order perturbation is a critical factor in achieving robust stability for uncertain linear systems.
- The proposed probabilistic method provides a systematic way to determine optimal fractional orders for robust stabilization.
- The developed algorithm offers a practical solution for robust stabilization problems in interval uncertain systems.
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