Robust H₂ and H_∞ Filter Design for Continuous‐time Uncertain Linear Fractional Transformation Systems via LMI

Abstract

This paper considers the problem of robust H 2 and H ∞ filter design for uncertain continuous-time linear systems. Linear fractional transformation (LFT) representation is considered for the uncertainty modeling and by definition of large number of slack variables, extra free dimensions are provided to the H 2 and H ∞ filter design optimization problem, so method presented in this paper expected to be less conservative than the existing methods for the polytopic uncertain systems and its efficiency for filter design is illustrated by means of numerical comparisons with some benchmark examples from the literature.

Improved robust filter synthesis combining linear matrix inequalities and heuristic algorithms

“…When dealing with parameter-dependent LMIs, it is known that Finsler lemma can be used to introduce extra decision variables to the LMI, enlarging the solution space and reducing the conservatism. 38,39 However, the restricted definition of  elements, as written in (22), reduces some of the available solution space. It is natural to notice that more relaxed results would be achieved if structure restrictions were not used; however, a challenging problem emerges, as introducing extra terms preclude solution by convex algorithms.…”

“…Reduced order $$$ {\mathscr{H}}_2 $$$ and $$$ {\mathscr{H}}_{\infty } $$$ filters dedicated to positive uncertain systems are obtained in Reference 10 using an iterative procedure, which aims to reduce problem conservativeness by introducing a relaxation in solution variables. In Reference 22, auxiliary and slack variables are introduced to the $$$ {\mathscr{H}}_2 $$$ and $$$ {\mathscr{H}}_{\infty } $$$ filter problem, improving filtering performance. It is possible to notice that, although the mentioned works have demonstrated improvements in filter synthesis, some are still relying on limited convexification techniques at some point, obtained by restricting some free elements and using slack variables.…”