On the synthesis of linear H∞H∞ filters for polynomial systems

This paper is concerned with the H∞H∞ filtering problem for polynomial systems. By means of Lyapunov theory and matrix inequality techniques, sufficient conditions are first obtained to ensure that the filtering error system is asymptotically stable and satisfies H∞H∞ performance constraint. Then, a sufficient condition for the existence of desired filters is established with a free matrix introduced, which will greatly facilitate the design of filter matrices. By virtue of sum-of-squares (SOS) approaches, a convergent iterative algorithm is developed to tackle the polynomial H∞H∞ filtering problem. Note that the approach can be efficiently implemented by means of recently developed SOS decomposition techniques, and the filter matrices can be designed explicitly. Finally, a numerical example is given to illustrate the main results of this paper.