By using the definition of positive and negative definite matrices and stability theory of fractional-order systems, sufficient conditions for robust stabilization of closed-loop perturbed fractional-order linear interconnected systems are given.
By using the definition of the retardation coefficient and the statistical crack growth law, retardation cycles after an overload are predicted.
A numerical model for the effective thermal conductivities of multiaxial non-woven composites (NWCs) was derived by using the definition of thermal resistance.
The optimization of the structural design of wind turbines for such applications requires a risk analysis that is made by using the definition of return periods of extreme events with respect to the lifespan of wind turbines.
The constitutive elasto-plastic matrix and its components are derived by using the definition of yield surface, material functions and non-linear elastic behavior, as function of hardening parameters.
By using the definition, we have (5.55).
Indeed, by using the definition of, we have (3.4).
(ii) By using the definition, easy to prove.
Hence, by using the definition of and applying Theorem A1, we obtain (4.34).
But by using the definition of in (5.44) the proof of the lemma is complete.
To develop this transformation, we begin by using the definition of the instantaneous cross-correlation (5).
