Abstract
<abstract><p>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 $.</p></abstract>
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