## Displaying similar documents to “On the extension of Rosenbrock's theory in algebraic design on multivariable controllers.”

### Some remarks on a problem of C. Alsina.

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Equation [1] f(x+y) + f (f(x)+f(y)) = f (f(x+f(y)) + f(f(x)+y)) has been proposed by C. Alsina in the class of continuous and decreasing involutions of (0,+∞). General solution of [1] is not known yet. Nevertheless we give solutions of the following equations which may be derived from [1]: [2] f(x+1) + f (f(x)+1) = 1, [3] f(2x) + f(2f(x)) = f(2f(x + f(x))). Equation [3] leads to a Cauchy functional equation: ...

### Representation of continuous associative functions.

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Strengthened forms of Ling's representation theorem concerning a class of continuous associative functions are given: Firstly the monotonicity condition is removed. Then the associativity condition is replaced by the power associativity.

### Imprecise notions in individual and group decision theory: Resolutions of Allais paradox and related problems.

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This paper deals with two ways in which uncertainty notions enter social science models: 1) They can be used in an effort to make intelligible some phenomena that would otherwise be difficult to comprehend, or 2) They can be use to generalize or modify the domain of validity of some theoretical results.

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### Integral equations and time varying linear systems.

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In this paper we study the resolution problem of an integral equation with operator valued kernel. We prove the equivalence between this equation and certain time varying linear operator system. Sufficient conditions for solving the problem and explicit expressions of the solutions are given.

### A theorem on implication functions defined from triangular norms.

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Several transformation which enable implication functions in multivalued logics to be generated from conjunctions have been proposed in the literature. It is proved that for a rather general class of conjunctions modeled by triangular norms, the generation process is closed, thus shedding some light on the relationships between seemingly independent classes of implication functions.

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### On symmetries and parallelogram spaces.

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The notion of a TST-space is introduced and its connection with a parallelogram space is given. The existence of a TST-space is equivalent to the existence of a parallelogram space, which is a new characterization of a parallelogram space. The structure of a TST-space is described in terms of an abelian group.