Minimization of the estimation error of the Kalman filter with an H ∞ error bound by Secant method

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 be sustained. Furthermore, the uniqueness, as opposed to the H_∞ filter, of the filter is applied 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 the 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