An overview of polynomic system theory

Abstract

s from Papers Appearing in the Proceedings of the IEEE, Special Issue-JanuaT 1976 An Overview of Polynomic System Theory @ W. A. PORTER Department qf ELectrical Engineering, University of Michigan, Ann Arbor, Michigan ABSTRACT: During the past 5 yr multilinear, multipower and polynomic systems have become a most important area of applications and theoretical development. This paper starts with some typical examples and historical remarks. Using this background, it then proceeds to put the recent literature in perspective and to quantify partially some broad problem categories wh,ere intensive work is underway. During the past 5 yr multilinear, multipower and polynomic systems have become a most important area of applications and theoretical development. This paper starts with some typical examples and historical remarks. Using this background, it then proceeds to put the recent literature in perspective and to quantify partially some broad problem categories wh,ere intensive work is underway. Scattering Theory and Linear Least Squares Estimation Part I: Continuous-time Problems by L. LJUNG, T. KAILATH and B. FRIEDLANDER Information Systems Laboratory Department of Electrical Engineering Stanford University, California ABSTRACT : The Riccati equation plays an equally important role in scattering theory as in linear least-squares estimation theory. However, in the scattering literature, a somewhat cllffererrt ~frarnework of treatgnz,ple rlerl’cations of known results as well as to obtain several new results. Examples include the derivation of backwards equations to solve forwards Riccati equations; an analysis of the asymptotic behaviour of the Riccati equation; the derivation of backwards Markovian representations of stochastic processes; and new derivations and new insights into the Chandrasekhar and related Levinson and Cholesky equatioras. The Riccati equation plays an equally important role in scattering theory as in linear least-squares estimation theory. However, in the scattering literature, a somewhat cllffererrt ~frarnework of treatgnz,ple rlerl’cations of known results as well as to obtain several new results. Examples include the derivation of backwards equations to solve forwards Riccati equations; an analysis of the asymptotic behaviour of the Riccati equation; the derivation of backwards Markovian representations of stochastic processes; and new derivations and new insights into the Chandrasekhar and related Levinson and Cholesky equatioras.