A New Design of Robust H2 and H∞ Filter for Discrete-time Uncertain Systems

In this article, the problem of robust
$H$
2
and
$H$
∞
filter design for discrete-time systems with polytopic parameters is studied. First, the dimension of filter design matrices are dilated. For
$H$
2
filter, the matrix is dilated from 3 to 4, and for
$H$
∞
filter, the corresponding matrix is dilated from 4 to 5. Then, the polynomial parameter-dependent method is applied to design the Lyapunov function and filter gains. In addition, an iteration algorithm is used to further reduce the conservativeness. The superiority of the proposed conditions is illustrated by some simulation examples borrowed from the literature.