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

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1 Author(s)
Bierman, G.J. ; Litton Systems Inc., Woodland Hills, CA, USA

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.

Published in:

Automatic Control, IEEE Transactions on  (Volume:16 ,  Issue: 2 )