Robust H 2 and H ∞ Filter Design for Polytopic Systems by Dilating Matrices

In this article, the problem of robust and filter design for linear systems with polytopic parameters is studied. First, the dimensions of filter design matrices are dilated. For filter, the matrix is dilated from 3 to 4, and for filter, the corresponding matrix is dilated from 4 to 5, such that more slack variables can be introduced. 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. Finally, the effectiveness and the superiority of the proposed conditions are shown by four examples.