Pareto optimal filter design with hybrid $ H_{2} /H_{\infty} $ optimization

Abstract

In this article, we study the Pareto optimal $ H_{2} $ /$ H_{\infty} $ filter design problem for a generalization of discrete-time stochastic systems. By constructing the estimation equation of the given systems with the estimated signal, a filter error estimation system is obtained. The aim is to obtain a gain matrix $ K^{\star} $ that optimizes both performance indicators we set. To deal with this problem, two different upper bounds for two performance indicators are given respectively. The optimal problem therefore is transformed into a Pareto optimal problem with linear matrix inequalities ($ LMIs $) which can be addressed through the $ LMI $ toolbox in $ MATLAB $.

Keywords

• $ {lmis} $
• $ h_{2}/h_{\infty} $ filter
• pareto optimality solutions
• multi-objective problem