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Reachability for interval max-plus linear systems
2017 36th Chinese Control Conference (CCC), 2017This paper proposes the interval max-plus linear system and introduces the reachability to such systems. A state of an interval max-plus linear system is said to be reachable if it can always be attainable from the initial state, no mater how the state and input matrices vary in a certain range. It is pointed out that an interval max-plus linear system
Cailu Wang, Yuegang Tao, Peng Yang
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An Interval Algorithm for Linear‐Nonlinear Coupled Systems
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1997AbstractIn this paper an interval algorithm for linear‐nonlinear coupled systems is described, and the convergence of the interval sequence is proved. The algorithm is composed of two steps of lower dimensional calculations, for large or sparse problems it is an efficient method.
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Robust stability of linear interval descriptor systems
Proceedings of the 36th IEEE Conference on Decision and Control, 2002This paper considers a class of descriptor systems with interval plants. It first derives a norm bound for uncertain descriptor systems to be impulse-free (regular) and asymptotically stable. Then, a necessary and sufficient condition for the uncertain linear interval descriptor systems to be structurally stable is established.
null Chong Lin +2 more
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Interval Gauss-Seidel Method for Generalized Solution Sets to Interval Linear Systems
Reliable Computing, 2001A Gauss-Seidel-type method, performed in Kaucher interval arithmetic, is used to enclose a generalized solution set of a linear interval system \({\mathbf A}x={\mathbf b}\). The method is shown to yield the optimal enclosure provided \({\mathbf A}\) is an interval \(M\)-matrix.
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Solving Interval Linear Systems is NP-Hard
1998In the previous chapter, we showed how to compute the range of a fractionally linear function f(x1,..., xn) on given intervals x1,..., xn in polynomial time. A fractionally linear function f(x1,...,xn) can be described as a solution of a linear equation (b0+Σbixi) · f = a0 + Σaixi. The problem of finding the range of f is thus equivalent to finding the
Vladik Kreinovich +3 more
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Extremal Results for Algebraic Linear Interval Systems
2016This chapter explores some important characteristics of algebraic linear systems containing interval parameters. Applying the Cramer’s rule, a parametrized solution of a linear system can be expressed as the ratio of two determinants. We show that these determinants can be expanded as multivariate polynomial functions of the parameters.
Daniel N. Mohsenizadeh +3 more
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Parallel interval methods for perturbed linear systems
1994The constants defining a system of linear equations may be subject to incertainties. In this case the induced variations of the solution can be effectively bounded by methods of interval analysis. In the worst case the complexity of this problem is exponential in the number of variables. We consider Rohn's sign-accord algorithm to solve the problem.
Kaj Madsen, Ole Toft
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Parameterized solution of linear interval parametric systems
Applied Mathematics and Computation, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Interval Linear Systems: Search for Feasible Classes
1998In the previous chapter, we showed that in general, solving interval systems is NP-hard. In this chapter, we look for feasible classes of interval linear systems.
Vladik Kreinovich +3 more
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