Designing a Kalman filter with a constraint on the H∞ norm of the estimation error was first developed by Bernstein and Haddad in 1989. The main result is a sufficient condition for characterizing the Kalman filter. Like the standard Kalman filter, the orthogonal principles are also shown to sustain. Furthermore, the uniqueness, as opposed to the H∞ filter, of the filter is implied by the orthogonal principles. In this paper, an approach to get the minimum energy with a constraint on the H∞ norm of the estimation error is proposed since the original work of Bernstein and Haddad does not, in general, reach the minimum energy of the estimation error. By means of Secant method, the energy of the estimation error can be reduced as minimum as possible, under the condition that the H∞ error bound is still satisfied.
|Number of pages||6|
|Journal||Proceedings of the IEEE Conference on Decision and Control|
|State||Published - 1 Dec 1995|
|Event||Proceedings of the 1995 34th IEEE Conference on Decision and Control. Part 1 (of 4) - New Orleans, LA, USA|
Duration: 13 Dec 1995 → 15 Dec 1995