On the design of observers for generalized state space systems using singular value decomposition

1 September 1983

journal article
research article
Published by Taylor & Francis in International Journal of Control

Vol. 38 (3) , 673-683
https://doi.org/10.1080/00207178308933101

Abstract

In this paper a method is developed for the design of Luenberger-type observers for linear time-invariant control systems whose state equation is of the form Ex= Ax+ Bu where E is a singular square matrix. The method is based on the singular-value decomposition of the matrix E, and on the reduction of the equation Ex= Ax +Bu to a system consisting of a differential equation of the form w₁, = F₁w₁ + F₂ + w₂ +G₁u and an algebraic equation of the form H₁w₁ +H₂w₂ + G₁u = 0. If w₂ can be eliminated from the differential equation by the aid of the algebraic equation and the original output equation of the system, the method yields a reduced-order observer for the generalized state space system.

Keywords

This publication has 7 references indexed in Scilit:

A generalized state-space for singular systems
IEEE Transactions on Automatic Control, 1981
On the application of matrix generalized inverses to the design of observers for time-varying and time-invariant linear systems
IEEE Transactions on Automatic Control, 1980
The singular value decomposition: Its computation and some applications
IEEE Transactions on Automatic Control, 1980
An introduction to the application of the simplest matrix-generalized inverse in systems science
IEEE Transactions on Circuits and Systems, 1978
On rectangular systems of differential equations and their application to circuit theory
Journal of the Franklin Institute, 1975
Linear Least Squares Solutions by Housholder Transformations
Published by Springer Nature ,1971
Calculating the Singular Values and Pseudo-Inverse of a Matrix
Journal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis, 1965