Reduced Order Positive Filter Design for Positive Uncertain Discrete-Time Linear Systems

Improved robust filter synthesis combining linear matrix inequalities and heuristic algorithms

“…Filtering problems usually involve uncertainties and additional performance indexes, such as the $$$ {\mathscr{H}}_2 $$$ and $$$ {\mathscr{H}}_{\infty } $$$ norms. Recent works exploring $$$ {\mathscr{H}}_2 $$$ and $$$ {\mathscr{H}}_{\infty } $$$ guaranteed costs for filtering and fault detection can be mentioned, 7‐10 as well as control problems 11‐13 . The solution of $$$ {\mathscr{H}}_2 $$$ and $$$ {\mathscr{H}}_{\infty } $$$ problems are often initially modeled as a set of bilinear matrix inequalities (BMIs), which are NP‐hard and, thus, difficult to solve 14 .…”

“…In Reference 21, a sequential convex approximation is applied, in which BMI constraints are initially converted to LMIs, iteratively solved to obtain filter parameters. 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.…”