Container of (min, +)-linear systems

2010

We will present sufficient conditions for the Fredholm property of Wiener-Hopf plus and minus Hankel operators with different Fourier matrix symbols in the C * -algebra of semialmost periodic elements. In addition, under such conditions, we will derive a formula for the sum of the Fredholm indices of these Wiener-Hopf plus Hankel and Wiener-Hopf minus Hankel operators. Some examples are provided to illustrate the results of the paper.

2008 9th International Workshop on Discrete Event Systems, 2008

This paper deals with the computation of a maximal flow in single input single output (max, +) linear systems. Assuming known a system composed of some subsystems -each one being described by a transfer functionand some secondary inputs interfering with the principal flow on consecutive sub-systems, the computation of a maximal principal output is addressed. Transfer functions, inputs and outputs are represented by periodical series in a semiring of formal series, namely N min δ . Previously, it is shown that the Hadamard product of such series allows to compute the addition of inputs, and that this product is both residuated and dually residuated. These properties are used to compute the maximal principal output. An example concludes the paper and allows to illustrate the efficiency of the proposed approach.

Linear Algebra and its Applications, 1992

Given an input-output periodic application, we prove that a periodii realization is minimal if and only if it is reachable and observable. We define the block Hankel matrix associated with the input-output periodic application, and we obtain the dimension of the minimal realization by means of the rank of it. This is the extension of the well-known result for the invariant case. Furthermore, we study similar periodic systems which are basic for getting minimal periodic realizations. 1.

Discrete Event Systems, 2000

Linear Algebra and its Applications, 2009

A ⊗ x b, where A, x and b are interval matrices with entries defined over idempotent semiring. It deals also with the computation of a pair of intervals, (x, y) which satisfies the equation A⊗x = B⊗y. It will be shown that this equation may be solved by considering the interval version of the iterative scheme proposed in [7].

The main purpose of this paper is to propose six programs in C ++ for matrix computations and solving recurrent equations systems with entries in min plus algebra. 1 1 AMS classification: 15A80, 68-04. Key words and phrases: idempotent semiring, min plus algebra. 1. the sum of two matrices A, B ∈ M m×n (R min); 2. the product of two matrices A ∈ M m×n (R min) and B ∈ M n×p (R min); 3. the product of a a scalar α ∈ R min with a matrix A ∈ M m×n (R min); 4. the power of a matrix A ∈ M n×n (R min); 5. ∆ 1 (A) and ∆ 1 (A) for A ∈ M n×n (R min) when n = 2 and n = 3; 6. the solving a linear system of the form: X(k + 1) = A ⊗ X(k), k ≥ 0, where A ∈ M n×n (R min) and X(k) ∈ M (n, 1; R min). Remark 3.1. In [4] are given five programs in C ++ for matrix computations in R max .✷ • We first give the Form1 Designer of program. name space Operations − with − matrices − in − min − plus − algebra { partial class Form1 {

Mathematische Nachrichten, 1978

Selecta Mathematica, 1998

Let K n = {x ∈ R n | x i ≥ 0, 1 ≤ i ≤ n} and suppose that f : K n → K n is nonexpansive with respect to the l 1 -norm, x 1 = n i=1 |x i |, and satisfies f (0) = 0. Let P 3 (n) denote the (finite) set of positive integers p such that there exists f as above and a periodic point ξ ∈ K n of f of minimal period p. For each n ≥ 1 we use the concept of "admissible arrays on n symbols" to define a set of positive integers Q(n) which is determined solely by number theoretical and combinatorial constraints and whose computation reduces to a finite problem. In a separate paper the sets Q(n) have been explicitly determined for 1 ≤ n ≤ 50, and we provide this information in an appendix. In our main theorem (Theorem 3.1) we prove that P 3 (n) = Q(n) for all n ≥ 1. We also prove that the set Q(n) and the concept of admissible arrays are intimately connected to the set of periodic points of other classes of nonlinear maps, in particular to periodic points of maps g : Dg → Dg, where Dg ⊂ R n is a lattice (or lower semilattice) and g is a lattice (or lower semilattice) homomorphism.

2020

In this paper we compute the closure of the numerical range of certain periodic tridiagonal operators. This is achieved by showing that the closure of the numerical range of such operators can be expressed as the closure of the convex hull of the uncountable union of numerical ranges of certain symbol matrices. For a special case, this result can be improved so that it is the convex hull of the union of the numerical ranges of only two matrices. A conjecture is stated for the general case.

New Trends in Design of Control Systems 1994, 1995

A general framework based on operators on sequences is presented. It is shown that it is very suitable for the description of periodic system. With it two liftings are derived which enable to represent a periodic system by a time invariant one. Conections are also made to the notion of operational transfer functions, and more generally the operational transfer inclusion. The realization of periodic systems from their impulse response data is given. Finally, this framework is shown to be advantageous in the computation of robust periodic controllers for time-invariant systems.