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About Robust Stability of Caputo Linear Fractional Dynamic Systems with Time Delays through Fixed Point Theory
Fixed Point Theory and Applications volume 2011, Article number: 867932 (2011)
This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The investigation is performed via fixed point theory in a complete metric space by defining appropriate nonexpansive or contractive self-mappings from initial conditions to points of the state-trajectory solution. The existence of a unique fixed point leading to a globally asymptotically stable equilibrium point is investigated, in particular, under easily testable sufficiency-type stability conditions. The study is performed for both the uncontrolled case and the controlled case under a wide class of state feedback laws.
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De la Sen, M. About Robust Stability of Caputo Linear Fractional Dynamic Systems with Time Delays through Fixed Point Theory. Fixed Point Theory Appl 2011, 867932 (2011). https://doi.org/10.1155/2011/867932
- Equilibrium Point
- Asymptotic Stability
- Fractional Order
- State Feedback
- Point Theory