Improved scalar parameters approach to design robust H∞ filter for uncertain discrete-time linear systems

This note investigates the less conservative robust H∞ filtering for uncertain discrete-time systems from the point of view of structured scalar parameters approach. To increase the design degree of freedom, a new structure characterized by the diagonal matrix multipliers composed of independent scalar parameters is proposed on the basis of eigenvalues theory when defining auxiliary matrix variables. The merit of such idea can be guaranteed by optimally searching those multipliers of the slack matrix variables involved in the products with filter parameters in the design conditions. Then, this formulation is applied to improve the bounded and unbounded scalar parameters based results. Finally, three examples are given to illustrate the effectiveness and expansibility of the developed methods.