Section 5, which includes a fundamental theorem relating performance in the face of uncertainty to This paper introduces a nonconservative measure of the SSV. Section 6 provides an example, and Section performance for linear feedback systems in the face 7 contains concluding comments. of structured uncertainty. This measure is based on a new matrix function, which we call the Structured 2. Notation Singular Value. ??l.(k) = Algebra of complex kxk matrices 1. Introduction

After a review of the development of the Mayne-Fraser two-filter smoother, a first principle argument is used to rederive this smoother. Reversed-time Markov models play a key role in forming a state estimate from future observations. The built-in asymmetry of the MayneFraser smoother is pointed out, and it is shown how this asymmetry may be removed. Additionally, a covariance analysis of the two-filter smoother is provided, and reduced-order smoothers are analyzed.

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