Algebraic modelling of linear systems by means of Walsh functions

Konigorski, Ulrich

doi:10.1080/13873950500067064

Cited by 3 publications

(1 citation statement)

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“…3 The matrix A 2 F nÂn 2 is the dynamics of the system, and the matrix B 2 F nÂm 2 is the input matrix. At first, we examine linear systems with B ¼ 0, according to the simplest automaton description in (22), that is…”

Section: Analysis Of Autonomous Linear Modular Systemsmentioning

confidence: 99%

A Finite Field Framework for Modeling, Analysis and Control of Finite State Automata

Reger

Schmidt

2004

Mathematical and Computer Modelling of Dynamical Systems

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In this paper, we address the modeling, analysis and control of finite state automata, which represent a standard class of discrete event systems. As opposed to graph theoretical methods, we consider an algebraic framework that resides on the finite field F 2 which is defined on a set of two elements with the operations addition and multiplication, both carried out modulo 2. The key characteristic of the model is its functional completeness in the sense that it is capable of describing most of the finite state automata in use, including non-deterministic and partially defined automata. Starting from a graphical representation of an automaton and applying techniques from Boolean algebra, we derive the transition relation of our finite field model. For cases in which the transition relation is linear, we develop means for treating the main issues in the analysis of the cyclic behavior of automata. This involves the computation of the elementary divisor polynomials of the system dynamics, and the periods of these polynomials, which are shown to completely determine the cyclic structure of the state space of the underlying linear system. Dealing with nonautonomous linear systems with inputs, we use the notion of feedback in order to specify a desired cyclic behavior of the automaton in the closed loop. The computation of an appropriate state feedback is achieved by introducing an image domain and adopting the well-established polynomial matrix method to linear discrete systems over the finite field F 2 . Examples illustrate the main steps of our method.

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Section: Analysis Of Autonomous Linear Modular Systemsmentioning

confidence: 99%