The robustness of interval matrices in max-plus algebra
نویسندگان
چکیده
منابع مشابه
Eigenvectors of interval matrices over max-plus algebra
The behaviour of a discrete event dynamic system is often conveniently described using a matrix algebra with operations max and plus Such a system moves forward in regular steps of length equal to the eigenvalue of the system matrix if it is set to operation at time instants corresponding to one of its eigenvectors However due to imprecise measurements it is often unappropriate to use exact mat...
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Fuzzy algebra is an algebraic structure in which classical addition and multiplication are replaced by ⊕ and ⊗, where a⊕ b = max{a,b}, a⊗ b = min{a,b}. Fuzzy discrete dynamic systems can be introduced by fuzzy matrices and are useful for describing knowledge engineering, scheduling, cluster analysis, fuzzy logic programs, diagnosis of technical devices or medical diagnosis. The paper deals with...
متن کاملMax-plus algebra
The max-plus semiring Rmax is the set R∪{−∞}, equipped with the addition (a, b) 7→ max(a, b) and the multiplication (a, b) 7→ a + b. The identity element for the addition, zero, is −∞, and the identity element for the multiplication, unit, is 0. To illuminate the linear algebraic nature of the results, the generic notations +, , × (or concatenation), 0 and 1 are used for the addition, the sum, ...
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In general semimodules, we say that the image of a linear operator B and the kernel of a linear operator C are direct factors if every equivalence class modulo C crosses the image of B at a unique point. For linear maps represented by matrices over certain idempotent semifields such as the (max,+)-semiring, we give necessary and sufficient conditions for an image and a kernel to be direct facto...
متن کاملOn the sequence of consecutive matrix powers of boolean matrices in the max-plus algebra
If you want to cite this report, please use the following reference instead: B. De Schutter and B. De Moor, “On the sequence of consecutive matrix powers of boolean matrices in the max-plus algebra,” in Theory and Practice of Control and Systems (Proceedings of the 6th IEEE Mediterranean Conference on Control and Systems, Alghero, Italy, June 1998) (A. Tornambè, G. Conte, and A.M. Perdon, eds.)...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2014
ISSN: 0024-3795
DOI: 10.1016/j.laa.2013.12.008