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Practical stability analysis of fractional-order impulsive control systems.
Ivanka Stamova1, Johnny Henderson2
1Department of Mathematics, The University of Texas at San Antonio, One UTSA Circle, San Antonio, TX 78249, USA.
ISA Transactions
|June 14, 2016
Summary
This study establishes conditions for the practical stability of nonlinear fractional-order systems with impulse effects. It also presents a method for designing impulsive control laws to stabilize such systems.
Area of Science:
- Nonlinear dynamics
- Fractional calculus
- Control theory
Background:
- Fractional-order systems are increasingly studied for their complex dynamics.
- Impulse effects introduce challenges in analyzing system stability.
- Practical stability is a crucial concept for real-world system performance.
Purpose of the Study:
- To derive sufficient conditions for the practical stability of nonlinear fractional-order systems with impulse effects.
- To propose a design methodology for impulsive control laws.
- To practically stabilize fractional-order systems that are free of impulses.
Main Methods:
- Analysis of nonlinear differential equations of fractional order.
- Application of stability theory for systems with impulse effects.
- Development of control law design techniques.
Main Results:
- Sufficient conditions for practical stability were successfully obtained.
- A design method for impulsive control laws was established.
- The proposed control law effectively stabilizes the impulse-free fractional-order system.
Conclusions:
- The derived conditions are adequate for ensuring practical stability.
- The impulsive control law design is a viable approach for stabilization.
- This work contributes to the understanding and control of fractional-order dynamical systems.
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