Robust filtering for discrete-time systems with bounded noise andparametric uncertainty
El Ghaoui, L.; Calafiore, G.
Automatic Control, IEEE Transactions on
Volume 46, Issue 7, Jul 2001 Page(s):1084 - 1089
Digital Object Identifier   10.1109/9.935060
Summary:This note presents a new approach to finite-horizon guaranteed state prediction for discrete-time systems affected by bounded noise and unknown-but-bounded parameter uncertainty. Our framework handles possibly nonlinear dependence of the state-space matrices on the uncertain parameters. The main result is that a minimal confidence ellipsoid for the state, consistent with the measured output and the uncertainty description, may be recursively computed in polynomial time, using interior-point methods for convex optimization. With n states, l uncertain parameters appearing linearly in the state-space matrices, with rank-one matrix coefficients, the worst-case complexity grows as O(l(n + l)^3.5) With unstructured uncertainty in all system matrices, the worst-case complexity reduces to O(n^3.5)

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