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Continuous variation in the operating point is tackled by an interval plant model where RS problem is reduced to simultaneous stabilization of finite number of plants according to Kharitonov theorem.
Therefore, the formulated K-user RS problem is a more general problem.
It can be easily extended to solve the K-user generalized RS problem.
We further extend it to solve the generalized RS problem (20).
The robust approach for 1-layer RS in [28] can be easily extended to solve the K-user generalized RS problem based on our proposed Algorithm 1, which will not be explained here.
Theorem 4. The SPR- RS problem can be solved in O kn) time.
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This discussion has led to the development of what is now known in the literature as the Zhou-Rozvany (Z-R) problem.
The Z-R problem is solved for both stress minimisation and minimum compliance, further highlighting the flexibility of the proposed formulation.
Finally, this paper aims to give some new insights into the uniqueness of the Z-R problem and to discuss the reasons for which discrete methods struggle to find suitable global optima.
Consider the tree R = SPR T (v, rt(T)) Observe that, since SPR R (v) = SPR S (v), solving the SPR-RS problem on instance ⟨(S), T, v⟩ is equivalent to solving it on the instance ⟨(S), R, v⟩.
In particular, we first show that any instance of the TBR-RS problem can be decomposed into an instance of an SPR-RS problem, and an instance of a Rooting problem (defined in the next section).
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