Finite series solutions for the transition matrix and the covariance of a time-invariant system

Author

Bierman, G.J.

Author_Institution

Litton Systems Inc., Woodland Hills, CA, USA

Volume

Issue

fYear

1971

fDate

4/1/1971 12:00:00 AM

Firstpage

173

Lastpage

175

Abstract

The transition matrix $\\varphi$ corresponding to the $n$ -dimensional matrix $A$ can be represented by $\\varphi (t) = g_{1}(t)I + g_{2}(t)A + ... + g_{n}(t)A^{n-1}$ , where the vector $g^{T} = (g_{1}, ... , g_{n})$ is generated from $\\dot{g}^{T} = g^{T}A_{c}, g^{T}(0) = (1, 0, ... , 0)$ and Acis the companion matrix to $A$ . The result is applied to the covariance differential equation $\\dot{C} = AC + CA^{T} + Q$ and its solution is written as a finite series. The equations are presented in a form amenable for implementation on a digital computer.

Keywords

Covariance matrices; Linear systems, time-invariant continuous-time; Matrix functions; Control systems; Covariance matrix; Differential equations; Eigenvalues and eigenfunctions; Estimation theory; Frequency domain analysis; Linear systems; Stochastic systems; Symmetric matrices; Time domain analysis;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1971.1099668

Filename

1099668

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=805501