Steady-state Kalman filtering with an H∞ error bound
Systems & Control Letters
On regional nonlinear H∞ -filtering
Systems & Control Letters
Turning points in interaction with computers
IBM Systems Journal
Brief H∞ controller reduction for nonlinear systems
Automatica (Journal of IFAC)
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In this article, sufficient conditions are presented for the existence of an H∞ filter with a state dimension less than the plant. The conditions are characterised in terms of the solution to a Hamilton-Jacobi inequality, which is exactly the one used in the construction of the full-order H∞ filters. When these conditions hold, state-space formulae are also given for such reduced-order filters. Both affine and general non-affine non-linear systems are examined. The development uses only elementary concepts of dissipativity and differential game, thus the given proofs are simple and clear. To illustrate our result, some numerical examples are also included.