A contraction analysis of risk-sensitive Riccati equations is proposed. When
the state-space model is reachable and observable, a block-update
implementation of the risk-sensitive filter is used to show that the N-fold
composition of the Riccati map is strictly contractive with respect to the
Riemannian metric of positive definite matrices, when N is larger than the
number of states. The range of values of the risk-sensitivity parameter for
which the map remains contractive can be estimated a priori. It is also found
that a second condition must be imposed on the risk-sensitivity parameter and
on the initial error variance to ensure that the solution of the risk-sensitive
Riccati equation remains positive definite at all times. The two conditions
obtained can be viewed as extending to the multivariable case an earlier
analysis of Whittle for the scalar case.Comment: 22 pages, 6 figure
