Computing difference abstractions of linear equation systems

Abstractions of Constrained Linear Systems

ions of Constrained Linear Systems Herbert G. Tanner University of Pennsylvania George J. Pappas University of Pennsylvania, [email protected] Follow this and additional works at: http://repository.upenn.edu/ese_papers Copyright 2003 IEEE. Reprinted from Proceedings of the American Control Conference 2003, Volume 4, pages 3381-3386. This material is posted here with permission of the IEEE....

FUZZY LOGISTIC DIFFERENCE EQUATION

In this study, we consider two different inequivalent formulations of the logistic difference equation $x_{n+1}= beta x_n(1- x_n), n=0,1,..., $ where $x_n$ is a sequence of fuzzy numbers and $beta$ is a positive fuzzy number. The major contribution of this paper is to study the existence, uniqueness and global behavior of the solutions for two corresponding equations, using the concept of Huku...

Approximately Bisimilar Finite Abstractions of Stable Linear Systems

The use of bisimilar finite abstractions of continuous and hybrid systems, greatly simplifies complex computational tasks such as verification or control synthesis. Unfortunately, because of the strong requirements of bisimulation relations, such abstractions exist only for quite restrictive classes of systems. Recently, the notion of approximate bisimulation relations has been introduced, allo...

Using Abstractions for the Verification of Linear Hybrid Systems

Finite Abstractions of Max-Plus-Linear Systems: Theory and Algorithms

ion function f , i.e. f−1(ŝ) = {s : f (s) = ŝ}. Recall that f−1(ŝ) is a block (or in fact a DBM) and the dynamics in each block are affine. If there exists a transition from an outgoing state s to an incoming state s′ in the concrete transition system, i.e. s γ −−→ s′, then there is a transition from f (s) to f (s′) in the abstract transition system, i.e. f (s) γ −−→ f f (s′) [23, Def. 7.51]. S...