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About robust stability of Caputo linear fractional dynamic systems with time delays through fixed point theory. (English) Zbl 1219.34102
Summary: 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.
MSC:
34K37Functional-differential equations with fractional derivatives
34K06Linear functional-differential equations
34K20Stability theory of functional-differential equations
47N20Applications of operator theory to differential and integral equations
34K35Functional-differential equations connected with control problems
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