There are many Cloud Service Providers (CSPs) in the global cloud computing market and customers may need to use scientific decision making methods for evaluating and ranking the CSPs according to their own requirements. Among the several approaches that have been proposed to solve the CSPs evaluation and ranking problem, there are Multi Attribute Decision Making (MADM) methods. One of the most commonly used MADM method is Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS). In this paper, we extend the TOPSIS method by using the Minkowski distance. We propose an Extended TOPSIS (E-TOPSIS) approach by varying the parameter p in the Minkowski distance. The applicability of the proposed E-TOPSIS approach is presented in a case study for CSPs evaluation and ranking in relation to a set of Service Measurement Index -SMI criteria. An analysis of E-TOPSIS solutions and the CSPs order change relative to parameter p variation is realized. A comparison of the E-TOPSIS solutions with TOPSIS solution is presented.

If H ∞ control laws are built on high-order models, then reduced computational speed and memory problems are likely to arise. This article proposes an algorithm for computing H ∞ controllers which is similar to the Matlab procedure hinfsyn.m, but of low order. The method consists in introducing dependencies between the differential equations of the controller by means of a rank minimisation problem. As a consequence, all differential equations of the controller are expressed as a linear combination of a smaller number of differential equations. Redundant states are then removed.

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