Reduced-order filtering design for non-linear systems with H ∞ setting

Abstract

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.