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The strict convexity of the availability function is guaranteed as long as one of the extensive variables is fixed.
When the designer has no information on reciprocity types, implementability of an incentive-compatible social choice function is guaranteed if it satisfies an additional insurance property.
The privacy of the function is guaranteed by having the entire table encrypted by a precomputed set of public keys and transmitted to the other party.
The resulting closed-loop fuzzy system is robustly reliable stochastically stable, and the corresponding quadratic cost function is guaranteed to be no more than a certain upper bound for all admissible uncertainties, as well as different actuator fault cases.
The cost function is guaranteed to be non-incremental at each step; however, this method is also converges to a local minima which highly depend on the initial guess of the algorithm.
Uncertain state-delays rather than constant ones are considered in an explicit way, and then a stabilizing condition in an LMI (Linear Matrix Inequality) form is worked out for both offline controller design and online optimization, so that an artificial Lyapunov function is guaranteed to be non-increasing.
Secondly, the control laws and triggering mechanisms are synthesized so that a priori chosen performance levels (in terms of the original cost function) are guaranteed by design next to asymptotic stability and constraint satisfaction.
The feasibility of neural network approximation of unknown system functions is guaranteed over practical compact sets.
The existence of subgradients for convex functions is guaranteed by the following proposition, see [29].
In the following lemma, the existence of a (C^{infty}) function approximating Lipschitz continuous functions is guaranteed.
The meshfree method and IGA are coupled using the higher-order consistency condition in the physical domain so that the higher-order continuity of basis functions is guaranteed, and the topological complexity of the global volumetric parameterization for IGA to build the 3D geometry can be overcome.
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